[User]
How many points of intersection exist between the functions f(x) = (-3(-2sin(1πx - 2) + 2) + 2)/(2(-2sin(1πx - 2) + 2) + 1) and g(x) = (1x)/(-3x - 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2sin(3π(3x - 2) + 2) + 1 = -2x + 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1(-1sin(2πx - 2) - 2)^2 - 4(-1sin(2πx - 2) - 2) + 1 = 1x + 4 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2sin(2π((2x - 2)/(3x + 2))) + 1 and g(x) = (1x - 1)/(1x + 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (3(-3|x + 3| - 1) + 3)/(-1(-3|x + 3| - 1) - 2) and g(x) = -2x^2 + 4x - 4 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1cos(1π(4x^2 + 3x - 2) - 3) - 3 = -2x^2 - 4x - 5 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2sin(3π(2|x - 3| - 2) - 2) + 1 = 4x^2 - 4x + 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2sin(2π(3x - 1) - 3) - 2 = -1|x + 2| have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1sin(3π(3x^2 - 5x) - 2) = -5x - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3cos(2π(2|x + 2| + 2) + 3) + 1 and g(x) = 4x - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2|(2sin(2πx + 2) + 2) - 1| + 1 = 1x^2 + 3x - 5 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2(-3cos(1πx + 2) - 1) - 2 and g(x) = (-3x - 3)/(-2x) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 4(1x^2 - 2x - 4)^2 + 5(1x^2 - 2x - 4) - 2 and g(x) = -1x^2 + 5x + 4 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2|(2cos(2πx - 3) + 1) + 1| - 3 = 2x^2 - 4x + 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-3(2sin(2πx - 1) - 2) - 1)/(3(2sin(2πx - 1) - 2)) and g(x) = (3x - 3)/(2x - 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2|((-1x + 3)/(-2x + 3)) - 1| and g(x) = 1x^2 - 5x where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -4(-2sin(3πx - 3))^2 + 5(-2sin(3πx - 3)) - 4 and g(x) = -2|x - 2| - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1(1cos(2πx + 2))^2 + 2(1cos(2πx + 2)) - 1 = (2x - 3)/(-2x) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3(-3cos(3πx - 1) + 2) - 4 and g(x) = (-1x + 2)/(-1x - 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3cos(1π(-3x^2 + 3x - 1) - 3) + 2 and g(x) = -3x^2 - 5x intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2cos(3π(4x - 5) + 1) - 1 and g(x) = 5x - 5 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-2(-1cos(1πx + 1) + 1) - 2)/(2(-1cos(1πx + 1) + 1)) = -4x^2 + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2(2cos(2πx) + 1)^2 + 1(2cos(2πx) + 1) - 1 and g(x) = 3x^2 - 4x where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2|(1cos(3πx - 1) - 3)| + 1 and g(x) = -3|x + 2| - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1(-1cos(1πx - 3))^2 - 3(-1cos(1πx - 3)) - 3 = 1|x - 2| - 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1cos(3π((-2x)/(-3x + 4))) + 1 = 2|x - 2| have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2(2cos(3πx + 3) - 2)^2 - 4(2cos(3πx + 3) - 2) - 3 and g(x) = (-2x - 2)/(1x - 2) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2(3x^2 - 3x - 5)^2 - 4(3x^2 - 3x - 5) and g(x) = 1|x - 2| - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1cos(2π(3x + 5) + 2) + 3 and g(x) = -1x^2 + 4x + 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3sin(1π(-4x - 1) + 1) + 3 and g(x) = 5x^2 + 4 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-2(3sin(2πx + 2) + 3) + 3)/(2(3sin(2πx + 2) + 3)) and g(x) = 4x^2 - 5x - 4 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 4(-3cos(3πx - 1) - 2)^2 + 1(-3cos(3πx - 1) - 2) - 3 and g(x) = 1|x + 1| - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1sin(1π(2x - 5) - 3) + 3 and g(x) = (-3x - 1)/(-1x + 2) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 5(-1sin(3πx + 3) + 2)^2 - 3(-1sin(3πx + 3) + 2) - 5 and g(x) = 3|x - 1| + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2cos(3π((2x + 2)/(1x)) + 2) + 1 and g(x) = -3x + 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 5(2cos(2πx) - 2) + 1 and g(x) = 2x^2 - 4x - 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3cos(1π((-2x - 1)/(-1x - 2)) - 1) = -2x^2 - 3x have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3|(2sin(2πx + 1) - 3) + 3| and g(x) = -1x where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1(-2cos(2πx + 1) + 2) + 4 and g(x) = 3x^2 + 3x + 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-3(3sin(2πx + 1) - 1))/(2(3sin(2πx + 1) - 1) - 3) and g(x) = (-2x)/(-1x - 2) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3|(1sin(1πx + 2) - 2) + 3| + 3 and g(x) = -1x + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 4(-2sin(1πx - 2) + 3) + 5 = 2x^2 - 2x have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2sin(3π(-4x^2 + 2x - 2) + 2) - 2 = -2|x - 1| - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3|(3cos(3πx - 3) + 3) - 3| + 3 and g(x) = 5x + 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2|((-1x + 2)/(-2x + 3)) + 3| and g(x) = 4x^2 + 1x + 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2|((-1x - 3)/(-2x - 1)) + 3| + 3 and g(x) = -1|x + 1| - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 5(-2cos(2πx - 3) - 1) + 2 and g(x) = (1x)/(1x) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1sin(3π(3|x + 3| + 1) - 1) + 1 = 1x - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-2(-3sin(2πx + 3) + 2) + 2)/(3(-3sin(2πx + 3) + 2) - 2) and g(x) = (-2x + 2)/(-1x + 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1|(-3x^2 + 4x + 5) - 2| and g(x) = 2x - 4 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (2(-1x^2 - 5x + 1) - 1)/(2(-1x^2 - 5x + 1) + 2) and g(x) = 1x^2 + 5x - 4 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3cos(3π(-2|x + 2|) + 3) - 3 and g(x) = 1x - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (2(2cos(3πx + 1) + 3) + 2)/(-2(2cos(3πx + 1) + 3) + 3) and g(x) = -1x^2 - 4x - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2(-2sin(2πx + 2))^2 - 5(-2sin(2πx + 2)) - 2 and g(x) = 1x^2 - 4x + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2sin(1π((-3x + 3)/(3x - 2))) - 1 and g(x) = -2|x + 2| + 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 5(-3sin(1πx + 1) - 1) - 5 = (-3x + 3)/(2x) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2sin(3π(2x^2 + 2x) - 1) + 3 and g(x) = 2x - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1(-3sin(1πx + 1)) + 2 and g(x) = 1x + 5 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1cos(1π(-2|x + 1| - 1) + 1) + 1 and g(x) = (2x - 1)/(2x + 1) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3(-1sin(2πx - 2) + 2) - 2 and g(x) = 1x where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -4(3cos(3πx - 2) - 2) - 2 and g(x) = -1x + 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3|(-3sin(2πx + 1) - 2) + 2| - 1 and g(x) = (3x + 3)/(3x - 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 3sin(2π(-4x + 3) - 3) - 1 = 1|x + 3| - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (1(2sin(1πx)) + 1)/(-2(2sin(1πx)) + 3) and g(x) = 4x + 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1cos(2π(-1x^2 + 5x + 5) - 2) - 3 = -2x^2 - 3x + 5 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2cos(3π(-1x + 1) - 1) - 3 = -2|x + 1| have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2sin(3π(-3x - 5)) - 2 and g(x) = (3x + 1)/(-1x - 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1cos(1π(-2|x - 1| + 1) - 3) + 1 and g(x) = -1x^2 + 3x where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3|(-2sin(2πx + 2)) - 1| + 3 and g(x) = (3x - 3)/(1x + 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3(-2cos(3πx + 1) - 3)^2 - 2(-2cos(3πx + 1) - 3) - 2 and g(x) = -2x^2 - 5x + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (2(2cos(3πx + 2) - 1) + 3)/(-1(2cos(3πx + 2) - 1)) = -2x + 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3sin(3π(5x - 4) + 2) and g(x) = -3|x - 3| + 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3cos(1π(1|x + 1|) + 3) - 2 = -1x have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2sin(3π(3|x + 2| - 3) + 2) and g(x) = 4x^2 + 1x in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -4(-3cos(2πx) - 3)^2 - 1(-3cos(2πx) - 3) + 5 and g(x) = -5x^2 + 5x + 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (1(3cos(3πx + 3) - 1) + 1)/(-1(3cos(3πx + 3) - 1) + 2) and g(x) = -5x - 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1cos(2π(3x - 5) + 3) + 1 and g(x) = 3x - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (1(2sin(3πx + 1) - 1))/(-1(2sin(3πx + 1) - 1) - 1) and g(x) = 1x + 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2|(1cos(3πx - 3) - 3) + 1| - 2 = 3|x + 2| + 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2|(2cos(3πx - 3)) - 1| - 2 and g(x) = 1x^2 + 3x - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 5(3x^2 - 2x - 1)^2 - 4(3x^2 - 2x - 1) - 4 and g(x) = 3x + 5 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2cos(3π((1x + 1)/(-3x + 2)) + 2) - 2 and g(x) = 2x^2 - 3x - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1(1x^2 + 5x + 1)^2 + 3(1x^2 + 5x + 1) - 1 = (-2x + 1)/(1x + 3) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1|((1x - 3)/(1x - 2)) + 2| - 3 and g(x) = -2x^2 - 3x - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 4(-2sin(3πx) + 1)^2 + 5(-2sin(3πx) + 1) - 5 and g(x) = -4x^2 - 2x + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1(4x^2 + 4x - 4)^2 - 3(4x^2 + 4x - 4) - 1 and g(x) = 3|x + 2| + 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3cos(2π(5x^2 - 5x - 3) + 3) and g(x) = (2x)/(-1x + 2) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-1(2sin(3πx + 1) - 1) + 3)/(-1(2sin(3πx + 1) - 1) - 2) and g(x) = 2x^2 + 1x + 4 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1(3sin(1πx + 1))^2 - 2(3sin(1πx + 1)) - 3 and g(x) = 2x^2 - 5x - 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2cos(2π(2|x + 2| - 3)) + 3 = 2x^2 - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (3(-1cos(3πx + 1)) + 2)/(-2(-1cos(3πx + 1))) = -1|x - 3| - 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1(1sin(1πx - 3) + 2)^2 - 1(1sin(1πx - 3) + 2) - 2 and g(x) = (2x - 1)/(-1x - 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (1(3sin(2πx + 3)) + 1)/(-1(3sin(2πx + 3)) + 2) = (1x + 1)/(2x + 1) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -4(3sin(2πx - 2) - 1) + 1 = (1x + 3)/(3x + 1) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2sin(2π(-2|x + 3|)) - 1 and g(x) = 1x^2 - 5x in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-1(3sin(2πx - 3) + 1) - 2)/(3(3sin(2πx - 3) + 1) - 1) and g(x) = -5x - 4 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2(5x^2 - 2x - 4)^2 + 5(5x^2 - 2x - 4) + 1 and g(x) = (-3x - 2)/(3x - 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 3cos(2π(5x + 3) - 2) + 1 = 3x^2 - 3x + 4 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3sin(3π(2x^2 - 2x - 4) + 2) + 3 = 5x + 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3cos(1π(4x - 4) + 2) = 2x^2 + 5x - 5 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-3(5x^2 + 4x - 4) + 2)/(2(5x^2 + 4x - 4) - 1) and g(x) = -2x^2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2|(1sin(3πx + 1) + 3) - 2| - 2 and g(x) = -2x^2 + 4x - 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2sin(2π(2x^2 + 4x + 2) + 3) and g(x) = 1x^2 + 1x - 5 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 3(2sin(1πx + 1)) + 5 = (-2x - 1)/(2x - 1) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3(2cos(3πx + 2) + 3) - 4 = -3|x - 2| have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 4(2sin(2πx - 3) + 1)^2 - 5(2sin(2πx - 3) + 1) - 2 and g(x) = 4x + 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 3(1x^2 - 4x + 1)^2 - 4(1x^2 - 4x + 1) - 1 = (-2x - 3)/(2x + 3) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -4(2cos(1πx - 1)) + 2 = -1|x| + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3cos(1π(-3x - 1) + 1) + 1 = (-2x + 1)/(-1x + 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2sin(3π(2x^2 + 1x + 1)) + 2 = (-2x + 1)/(2x + 3) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (1(-3sin(3πx - 3) + 2) - 2)/(2(-3sin(3πx - 3) + 2) - 1) and g(x) = -2x - 5 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2cos(3π(-1|x - 1|)) - 3 and g(x) = (1x + 3)/(-1x + 2) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3(2sin(2πx - 3) + 1) and g(x) = 5x^2 - 1x + 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1(-3cos(2πx + 3) + 3)^2 + 5(-3cos(2πx + 3) + 3) - 2 and g(x) = 1|x + 3| intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1sin(1π((-3x - 2)/(2x - 3))) + 1 and g(x) = 3|x - 1| - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1cos(3π(-4x - 2) + 2) and g(x) = -3|x - 2| + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3cos(1π(-4x^2 - 2x + 1)) - 2 and g(x) = 2|x + 3| intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 4(5x^2 + 4x - 3)^2 + 3(5x^2 + 4x - 3) - 2 and g(x) = 2|x - 3| - 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (1(3cos(2πx + 2) + 1) + 1)/(3(3cos(2πx + 2) + 1) - 2) and g(x) = 1|x + 1| + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2|(-3sin(3πx - 2)) - 3| - 2 and g(x) = -1x^2 + 1x + 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -5(-1cos(1πx - 2) + 1) + 5 and g(x) = (-1x - 2)/(-1x) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 5(1cos(3πx + 1) - 3)^2 + 1 = 2|x - 3| have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (3(-1sin(3πx) - 3) + 3)/(-1(-1sin(3πx) - 3) + 3) and g(x) = 2|x + 2| - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 5(2cos(3πx) - 3) + 5 and g(x) = (-1x)/(2x + 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 4(-2sin(3πx + 2) - 1) + 2 and g(x) = 3|x + 1| + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3sin(2π(3x^2 - 1x)) - 1 and g(x) = -4x - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3sin(1π(-4x^2 + 1x - 4) + 3) and g(x) = (-3x - 2)/(-3x - 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3(3x^2 + 4x - 2)^2 + 4(3x^2 + 4x - 2) - 4 and g(x) = (3x + 1)/(3x - 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3cos(1π((3x + 1)/(-3x + 2)) + 1) + 3 and g(x) = -1x^2 + 2x + 5 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -4(1cos(3πx + 2) - 3)^2 - 3(1cos(3πx + 2) - 3) + 1 and g(x) = 4x - 4 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3cos(1π(-1x^2 + 4x + 1) + 3) = -1x^2 + 4x + 4 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-2(-2cos(2πx + 2)) + 1)/(2(-2cos(2πx + 2))) and g(x) = 2x^2 + 3x - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3cos(1π(-4x^2 - 3x - 2) + 3) + 3 and g(x) = 2x + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-1(2x^2 + 5x - 2) + 3)/(-2(2x^2 + 5x - 2) - 1) and g(x) = 1x^2 - 5x + 5 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3cos(2π(-1x - 3) + 1) = -3x - 4 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1cos(2π(1x^2 - 3x - 5) - 2) + 1 and g(x) = (-2x - 1)/(1x + 2) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 5(-2sin(2πx + 2))^2 - 2(-2sin(2πx + 2)) + 1 and g(x) = 2|x - 1| - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2cos(2π(-5x - 4) + 2) - 1 and g(x) = -1|x + 3| + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1(-2cos(1πx + 3) + 3)^2 - 4(-2cos(1πx + 3) + 3) - 5 = (-2x)/(3x) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 5(2sin(3πx + 3) - 1)^2 + 4(2sin(3πx + 3) - 1) - 3 = 2|x + 3| + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1(2cos(2πx + 1) + 1) - 4 and g(x) = -1x + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2cos(3π((-3x)/(-3x - 3))) and g(x) = (3x + 2)/(2x + 1) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-1(2sin(1πx) - 1) + 1)/(-2(2sin(1πx) - 1) + 1) and g(x) = 4x^2 + 5x + 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 3(-3cos(3πx - 2) - 3)^2 - 2(-3cos(3πx - 2) - 3) + 2 = 1x^2 - 5x + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2cos(3π(1x - 5) - 2) + 1 = 5x^2 + 5x + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 3(-2sin(2πx + 2))^2 - 4(-2sin(2πx + 2)) - 5 = -1x^2 + 5x + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3sin(2π(1|x - 1| + 2) - 1) - 2 and g(x) = (-1x - 1)/(-1x + 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2sin(2π(-1x - 3) + 3) - 3 and g(x) = -1x + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-2(3x^2 + 1x - 4))/(2(3x^2 + 1x - 4) - 1) and g(x) = -1x^2 + 3x + 4 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1(1cos(2πx + 3) + 2)^2 + 5 = 4x + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2sin(1π(-1|x + 3|) + 3) - 2 = (-1x + 1)/(1x + 3) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2|(-3sin(2πx + 1) + 2) + 3| + 2 = 3x - 5 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 5(-5x^2 + 3x + 4)^2 + 5(-5x^2 + 3x + 4) - 3 and g(x) = -2|x - 1| + 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2cos(2π(3x - 4)) - 2 and g(x) = -3|x + 3| - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3sin(1π(3|x - 1| - 1) - 1) - 2 and g(x) = (2x + 3)/(-1x + 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1sin(2π(-2x^2 + 2x - 2)) and g(x) = 1x + 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2(1sin(1πx + 1) - 3)^2 + 3(1sin(1πx + 1) - 3) + 4 and g(x) = 2|x| where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3cos(1π(3|x + 1| - 2) - 3) - 1 and g(x) = 1|x + 2| - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2|(3cos(2πx + 3))| + 2 and g(x) = 1x^2 - 2x - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (1(1sin(3πx + 3) + 1) + 1)/(3(1sin(3πx + 3) + 1)) and g(x) = (-2x)/(-3x + 1) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3cos(1π(1x^2 + 5x - 1) - 3) + 2 and g(x) = -3|x - 3| + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2sin(1π(-3|x| - 1) - 1) + 2 and g(x) = 2x^2 - 5x in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2cos(2π((2x - 2)/(-1x + 2))) and g(x) = -3|x - 1| + 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1sin(1π(5x^2 - 1x - 3) - 2) + 2 and g(x) = 5x^2 + 3x - 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1(-2sin(1πx - 3) - 3)^2 - 5(-2sin(1πx - 3) - 3) - 5 and g(x) = -2x + 5 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1sin(1π((2x - 2)/(-3x)) + 3) - 1 and g(x) = 3x^2 + 5x - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2cos(2π(2x^2 - 2x - 4) + 2) + 1 and g(x) = -5x - 4 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2sin(3π(2|x - 2|) - 2) and g(x) = 1x^2 - 1x - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 3sin(2π(-3x^2 - 2x - 1)) + 2 = (3x + 2)/(-2x - 3) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3cos(3π(-1|x + 3| - 1) - 2) and g(x) = (2x + 3)/(-3x - 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3|(5x^2 - 5) - 2| - 1 and g(x) = -2x + 4 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2sin(1π(5x^2 - 4x - 4) - 1) and g(x) = -2|x - 2| - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -4(2sin(3πx - 2) + 2) + 4 and g(x) = (-2x + 3)/(-1x) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1|(-3sin(3πx + 3)) + 2| + 3 and g(x) = -2x + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1cos(2π(-2x^2 - 1x - 5) + 2) + 1 = -3x^2 + 4x + 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2cos(2π((3x - 3)/(-2x + 1)) + 1) + 3 = -4x + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1sin(2π(-1|x - 3| - 2) - 3) and g(x) = (-1x - 1)/(-3x - 1) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-2(-1cos(2πx - 1)) + 1)/(3(-1cos(2πx - 1)) - 1) and g(x) = (2x - 2)/(-2x - 1) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2cos(2π((-3x - 2)/(-1x - 3))) + 2 and g(x) = -3|x + 2| + 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2cos(2π(-1x - 2) - 2) and g(x) = 3x^2 + 4x - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1(1cos(2πx) + 1)^2 - 2(1cos(2πx) + 1) - 3 and g(x) = -2|x - 1| - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2sin(3π(-1x - 3) - 3) + 3 = 3|x + 3| + 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1sin(2π(2|x - 3| - 2)) - 2 and g(x) = -5x^2 + 3x - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3sin(2π((1x - 1)/(-3x + 1)) - 2) - 3 and g(x) = -5x - 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1|(-3cos(3πx - 1) - 3) + 3| - 3 = -3x^2 + 1x + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3(-3x^2 - 1x + 2)^2 + 3(-3x^2 - 1x + 2) + 1 and g(x) = -2x^2 - 2x - 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1cos(2π(-1x - 4) - 2) + 2 and g(x) = (-2x - 2)/(-1x + 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1sin(1π((-1x + 1)/(3x + 3)) - 2) - 1 and g(x) = 1|x + 3| - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2cos(1π(3x - 2) - 2) - 1 and g(x) = 1|x - 1| - 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1(-3sin(2πx - 3) - 1)^2 + 1(-3sin(2πx - 3) - 1) + 3 and g(x) = 1x intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3sin(1π(1x + 3) + 1) and g(x) = (-1x - 2)/(-2x + 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2(2cos(1πx - 1) + 3) + 3 and g(x) = (-1x + 2)/(-1x - 1) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-1(1sin(1πx - 3) - 2) - 1)/(-2(1sin(1πx - 3) - 2) - 3) and g(x) = (1x + 3)/(-2x) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2cos(1π(-2|x + 3| + 2) - 1) - 1 = -2|x + 3| - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3cos(2π(5x + 4) - 1) - 2 and g(x) = -3|x - 1| + 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (3(2sin(3πx + 1) - 2))/(-2(2sin(3πx + 1) - 2) - 3) and g(x) = (-1x + 2)/(-1x + 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1(-2cos(1πx) + 1)^2 + 3(-2cos(1πx) + 1) and g(x) = 1|x + 1| - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1sin(3π(-1x^2 + 2) - 1) + 2 = (-1x - 1)/(-2x + 3) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-1(3sin(1πx + 2) - 2))/(-3(3sin(1πx + 2) - 2) - 2) and g(x) = -1x^2 - 4x - 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (1(-2sin(3πx - 2)) - 3)/(-1(-2sin(3πx - 2)) - 2) and g(x) = (1x - 2)/(3x + 2) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1cos(3π((-1x - 1)/(-1x - 3)) + 2) and g(x) = 2|x + 3| - 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3cos(1π(2|x - 3| - 3) - 1) + 3 and g(x) = -1x^2 - 1x + 4 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1|(-4x^2 + 4x + 5) - 2| + 2 and g(x) = 2|x + 2| + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3sin(3π(-5x^2 - 3x + 4) - 3) - 2 and g(x) = -4x^2 + 2x - 5 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2cos(3π(5x^2 - 5x - 3) + 2) - 2 and g(x) = 3x + 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-3(-3sin(1πx) - 2) + 1)/(1(-3sin(1πx) - 2)) and g(x) = -2x^2 - 1x - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1|(-5x^2 + 1) + 2| - 1 = -2|x + 2| + 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -5(-3sin(3πx + 1) + 2) and g(x) = 1x + 4 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1|(-3cos(1πx - 2) - 3) + 3| - 2 and g(x) = (2x + 3)/(3x + 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3cos(1π((1x)/(-2x + 3)) - 1) + 1 and g(x) = 2x intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-3(2cos(3πx) - 1) - 2)/(-2(2cos(3πx) - 1) + 3) and g(x) = (-1x + 2)/(1x - 2) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3|(-2sin(3πx) + 1) - 2| - 1 and g(x) = 3x in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3|((3x + 3)/(1x - 2)) + 3| - 1 and g(x) = 3|x| + 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3sin(1π(-1x^2 + 5x - 1) + 3) + 1 = 1x - 5 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2|(1sin(2πx + 3) + 3)| - 3 and g(x) = -1x - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1cos(3π((-3x - 2)/(1x + 1)) + 1) + 2 and g(x) = 1|x - 2| - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (2(1x^2 - 4x - 4) + 1)/(-2(1x^2 - 4x - 4) + 1) and g(x) = 2|x - 3| - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2sin(2π(1|x - 3| + 1) - 2) = -1x^2 - 4x have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2sin(3π(1|x - 1| - 1)) = -1|x - 1| + 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1cos(2π(-1x - 1) + 2) and g(x) = 3|x| - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2cos(3π(1|x + 1| - 1) + 2) - 1 = -2|x - 2| + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-3(1cos(1πx + 2)) - 2)/(1(1cos(1πx + 2)) + 2) and g(x) = (-1x + 2)/(-1x + 3) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1|(2|x + 2| - 3) + 1| + 1 = (3x + 3)/(-2x + 1) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2sin(1π(3x^2 - 4x + 3) - 2) - 1 and g(x) = -5x^2 - 2x + 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2cos(1π(-5x^2 - 3x + 3) - 2) - 2 and g(x) = -4x^2 - 5x + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3cos(2π(-3x^2 + 3x + 2)) - 2 and g(x) = -2|x + 3| - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1(1cos(1πx - 3) + 1) and g(x) = -1|x + 1| + 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (-1(2cos(1πx + 1) + 2) + 1)/(-3(2cos(1πx + 1) + 2) + 2) and g(x) = 1x + 5 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2sin(2π(2|x + 1| - 3) - 3) - 1 and g(x) = 2|x - 1| intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2(1cos(2πx - 3) - 1) + 4 and g(x) = 1|x| - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 5(1cos(2πx - 1) + 3) + 3 and g(x) = 5x + 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3(3sin(1πx - 3) - 1) and g(x) = -1|x| - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3sin(2π(-1x + 1)) + 2 = 1x - 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (1(2sin(3πx - 1) - 2) + 3)/(1(2sin(3πx - 1) - 2) + 2) and g(x) = -2|x| - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1(-1cos(1πx + 1) + 2)^2 + 1(-1cos(1πx + 1) + 2) = 3|x - 3| - 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2sin(1π(3x^2 - 4x - 3) + 2) and g(x) = (-1x - 1)/(-1x + 3) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3(-2|x - 1| + 2)^2 + 5(-2|x - 1| + 2) + 1 and g(x) = (-2x + 2)/(3x + 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1|(-3|x + 2| + 2) + 1| - 1 and g(x) = (3x - 1)/(2x - 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2cos(3π(-1x^2 - 4x - 5)) and g(x) = 2|x - 1| intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1(-2sin(3πx + 3) - 3)^2 - 2(-2sin(3πx + 3) - 3) + 2 and g(x) = (-2x)/(-2x - 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2(2sin(2πx + 2) + 1) - 5 = 2x - 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2(-1sin(2πx - 1) - 1)^2 + 5(-1sin(2πx - 1) - 1) - 1 and g(x) = 4x - 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2sin(1π((1x + 2)/(-1x)) - 3) + 3 and g(x) = (1x + 1)/(-3x) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1sin(3π(5x - 1)) + 3 and g(x) = (-1x - 2)/(1x - 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (3(-3sin(2πx - 3) + 2) - 2)/(-2(-3sin(2πx - 3) + 2) + 1) and g(x) = 3|x - 1| + 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3sin(1π(-1x^2 - 4x + 1)) and g(x) = 3x + 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2sin(3π((1x - 2)/(3x - 2)) - 3) + 2 and g(x) = (2x)/(-1x + 2) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3sin(1π(-2|x - 2| - 3) - 2) and g(x) = -3|x - 1| where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-1(3cos(2πx) + 2) + 3)/(-1(3cos(2πx) + 2) - 2) and g(x) = -1x^2 - 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2sin(3π(2|x - 1|) - 2) - 1 = 3|x - 2| - 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2cos(3π((1x - 2)/(3x + 3)) - 3) + 1 and g(x) = 3|x + 1| - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-1(-2sin(2πx + 3) - 2) + 3)/(-2(-2sin(2πx + 3) - 2) - 2) = 4x^2 - 2x + 4 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2(3sin(2πx - 2) - 1) - 2 and g(x) = 1x + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1cos(3π(3x + 5)) - 3 and g(x) = -2x^2 + 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1sin(3π(-2|x - 1| + 1) + 1) + 2 and g(x) = -1x - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2cos(2π(3|x + 3| - 2)) - 2 and g(x) = 4x where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3cos(1π((1x - 1)/(-3x - 1)) - 2) + 1 and g(x) = 5x + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -5(-2cos(3πx - 1) + 1)^2 + 2(-2cos(3πx - 1) + 1) = -3|x - 2| - 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -5(-2cos(2πx)) + 5 = 1x have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2(-2|x - 1| + 2)^2 + 5(-2|x - 1| + 2) and g(x) = 1|x + 3| - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1|(1sin(3πx))| + 2 and g(x) = (-1x - 3)/(-3x - 1) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2(-1cos(1πx - 1) + 2)^2 + 5 = -1x + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3cos(3π(-1|x - 1| - 1)) = (-3x)/(-1x + 3) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2cos(1π(2x^2 - 2x - 2) - 1) - 1 = 3x^2 - 3x - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 4(-3sin(2πx)) - 3 and g(x) = (-3x - 1)/(-2x + 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3sin(3π(-1|x + 3| - 3) - 2) and g(x) = -1x^2 - 5x + 4 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2|(-2sin(3πx + 3) - 2) + 3| + 3 and g(x) = 2x - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2(3|x| - 1)^2 + 3(3|x| - 1) + 5 and g(x) = (3x - 2)/(-3x - 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-2(2cos(2πx - 2) + 1) - 1)/(-1(2cos(2πx - 2) + 1) + 2) and g(x) = -2x + 4 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -4(-2cos(3πx) + 3) - 4 and g(x) = -3x^2 - 3x + 4 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3sin(2π(-1x^2 - 3x + 1) - 3) + 1 and g(x) = (-3x + 1)/(2x - 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3sin(1π((3x + 1)/(-2x + 3))) + 1 and g(x) = 1|x + 2| - 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2cos(2π(2|x + 3| - 3)) and g(x) = 3x^2 + 4x + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (2(-3cos(3πx + 1) - 2) + 2)/(-3(-3cos(3πx + 1) - 2)) = 1x^2 + 4x have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2|(2x + 1)| and g(x) = 1x^2 - 1x intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1sin(3π(4x^2 + 5x - 3)) and g(x) = -2x^2 - 5x - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3|(3sin(1πx + 1) - 3)| + 1 and g(x) = 2|x + 2| - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (1(3sin(1πx + 3) - 1) + 3)/(-3(3sin(1πx + 3) - 1) + 1) and g(x) = (-1x - 2)/(-3x) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2(1sin(2πx) - 2) - 3 and g(x) = -2x - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 3cos(2π((-3x - 1)/(2x + 2)) + 1) + 1 = 1|x| + 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3(-2sin(1πx + 2) + 1) and g(x) = (2x)/(1x) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -5(2sin(1πx + 3) - 1) + 1 and g(x) = 1x - 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2sin(3π(-4x - 5)) and g(x) = 5x^2 - 3x - 5 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3sin(1π(-5x + 4) + 3) - 2 = 2x^2 - 4x - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2sin(1π(4x - 4)) - 2 = 2|x + 3| - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -5(-2sin(2πx - 3))^2 - 4(-2sin(2πx - 3)) - 1 = (-3x + 1)/(3x + 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3sin(2π(3|x + 3| - 2) - 2) - 3 and g(x) = (-1x - 3)/(1x + 3) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -4(3cos(1πx - 1) + 3) and g(x) = -1|x - 1| - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -4(3cos(3πx + 3) + 1) + 3 and g(x) = 3x^2 + 5x - 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1(-3sin(2πx + 3) - 1)^2 + 3(-3sin(2πx + 3) - 1) - 4 and g(x) = -3x + 4 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2(4x^2 + 5x + 1)^2 + 3(4x^2 + 5x + 1) - 1 = (-2x)/(1x) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2(2x^2 - 3x - 5)^2 + 5(2x^2 - 3x - 5) + 2 and g(x) = -2x^2 + 3x + 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (1(3cos(1πx + 3) + 2) + 3)/(1(3cos(1πx + 3) + 2) + 1) and g(x) = 2|x| + 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (3(2sin(2πx - 1) + 2) - 1)/(1(2sin(2πx - 1) + 2) - 2) = 5x^2 + 4x + 4 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2(2sin(1πx - 2) + 2)^2 - 2(2sin(1πx - 2) + 2) and g(x) = -5x^2 - 1x - 5 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1sin(2π(4x^2 - 1x - 5) + 3) and g(x) = -5x^2 - 4x + 5 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3cos(1π(5x + 4) + 2) - 2 = 3|x + 3| have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1(1sin(3πx + 3) - 3)^2 + 2(1sin(3πx + 3) - 3) - 5 and g(x) = (-2x - 3)/(1x - 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1|(-2sin(2πx + 1) - 2) + 1| + 2 and g(x) = -1|x + 1| + 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 5(1|x - 2| - 3)^2 + 2(1|x - 2| - 3) - 5 = (-2x - 2)/(2x + 1) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2(3cos(3πx - 2) + 1)^2 + 2(3cos(3πx - 2) + 1) - 2 and g(x) = 1x - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3sin(1π(-1|x - 1| - 3) + 3) + 1 and g(x) = (-3x + 1)/(-1x - 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1cos(3π(2|x| - 3) - 2) - 3 = -2x - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2sin(3π(5x^2 + 2) - 3) + 1 and g(x) = 3x in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1(-1x^2 - 5x + 3)^2 + 4(-1x^2 - 5x + 3) + 4 and g(x) = -2|x + 2| - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1cos(3π(1x + 1) - 3) and g(x) = (1x)/(-2x) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3(3cos(1πx + 3) + 2) - 2 and g(x) = (2x)/(2x - 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -5(2|x + 1| - 1)^2 + 2(2|x + 1| - 1) + 2 and g(x) = 1|x + 1| intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2sin(1π(-2x + 2) - 2) - 1 and g(x) = -3x^2 - 2x where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3|(-1sin(3πx - 3) + 3)| - 1 and g(x) = -3|x + 2| intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2cos(2π(-2x + 3)) - 2 = -3|x - 1| have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3|(-3cos(1πx + 3) + 1) - 1| + 2 and g(x) = (-1x - 1)/(-3x + 2) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2sin(3π(-1x^2 + 1x + 2) - 3) - 2 = (1x - 3)/(-3x + 1) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2sin(2π(3|x - 2| - 3) + 1) - 3 and g(x) = -2|x + 3| + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 4(3sin(3πx + 2) - 2)^2 + 5(3sin(3πx + 2) - 2) + 4 and g(x) = 3|x + 3| - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3sin(3π(1x - 3)) + 3 = 5x^2 + 4x - 4 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3(2cos(3πx) - 2)^2 + 1(2cos(3πx) - 2) - 1 = -5x + 4 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-3(-2sin(3πx - 2) - 2) - 3)/(-1(-2sin(3πx - 2) - 2) + 3) and g(x) = (1x + 3)/(2x) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -4(-1sin(1πx) + 2)^2 + 4(-1sin(1πx) + 2) + 4 and g(x) = -4x + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (3(-2sin(2πx - 1) + 2) + 2)/(1(-2sin(2πx - 1) + 2) - 2) and g(x) = 4x - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2sin(1π(-5x^2 - 4x + 4)) - 2 and g(x) = 5x + 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2cos(1π(4x^2 + 5x) + 1) - 1 and g(x) = -3x^2 - 5x + 4 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 5(-1x^2 - 3x + 5)^2 + 5(-1x^2 - 3x + 5) - 5 and g(x) = (2x + 2)/(3x - 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2sin(3π(-3|x - 1| - 1) + 3) + 2 and g(x) = 1x^2 - 1x + 4 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3sin(2π(1x^2 + 3x - 2)) - 1 and g(x) = -1|x| + 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2cos(1π(-2|x - 1| - 3) - 2) - 3 and g(x) = -2x in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-2(1cos(2πx) - 1) + 3)/(-1(1cos(2πx) - 1) - 3) and g(x) = (-3x - 3)/(1x) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3sin(2π(2x - 1)) + 1 = (-2x - 2)/(3x - 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1|(-2x^2 + 3x + 5) - 1| - 1 and g(x) = 1|x| + 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 4(2sin(3πx + 3) + 1) + 3 and g(x) = (-2x - 3)/(-3x) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3((3x + 3)/(3x - 2))^2 + 1((3x + 3)/(3x - 2)) - 1 and g(x) = 1|x + 2| - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1sin(3π(1x^2 + 4x - 4)) - 3 and g(x) = (-2x + 1)/(1x + 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (1(-2cos(1πx - 1)) + 3)/(2(-2cos(1πx - 1)) + 3) = 2|x| - 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 3sin(2π(-1|x + 2| + 3)) = (-1x)/(-2x + 3) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 1sin(3π(-4x + 2)) and g(x) = (1x - 2)/(-2x + 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2sin(2π(1|x + 1| - 2) - 1) - 2 and g(x) = -1|x - 2| + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-1(3cos(3πx - 2) - 1) + 1)/(-2(3cos(3πx - 2) - 1) - 1) and g(x) = -4x + 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2(-1sin(3πx + 1) + 3) + 5 and g(x) = 2x^2 + 2x + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2|(-2cos(2πx - 1) - 1) + 1| - 1 and g(x) = -2|x - 3| + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2sin(1π(2|x - 1| + 1) - 2) - 3 and g(x) = (3x - 3)/(-3x - 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2sin(2π(-4x + 3)) - 3 and g(x) = -5x^2 + 3x + 5 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -5(4x^2 - 4x)^2 + 4 and g(x) = -3x^2 + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3sin(1π((-2x + 3)/(1x + 2))) - 1 = 3x^2 + 4x - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3cos(1π(-1x + 3) + 3) + 2 and g(x) = (-3x - 1)/(-1x - 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3(-4x^2 + 1)^2 - 2(-4x^2 + 1) + 4 and g(x) = 2|x - 3| - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2|(-3cos(3πx + 2) - 3) + 1| + 3 and g(x) = (2x)/(2x) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3(-3sin(2πx - 2) + 3)^2 + 5 = 2x^2 + 5x + 4 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2(-3cos(2πx - 3) + 3)^2 - 2(-3cos(2πx - 3) + 3) - 3 and g(x) = 4x + 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-1(-3cos(1πx - 2) + 2) + 3)/(-3(-3cos(1πx - 2) + 2) - 3) = -2x^2 + 1x have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2|(2sin(1πx + 3) - 3) + 2| = -1x - 4 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 4(2sin(1πx - 3) + 2)^2 + 5(2sin(1πx - 3) + 2) - 3 and g(x) = -1|x - 1| + 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3sin(2π(-1x^2 - 2x + 3) - 3) + 1 and g(x) = (-1x - 2)/(1x - 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1(-3cos(3πx - 3) - 1) + 3 and g(x) = 1x + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3cos(3π(2|x| - 2) + 1) + 3 = 1x^2 - 5x - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1sin(1π(-3|x| + 3) - 2) - 1 and g(x) = -1x - 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1cos(3π(5x^2 - 1x + 5) - 2) - 2 = 1x - 4 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = (1(-2x^2 - 5x + 2))/(-2(-2x^2 - 5x + 2) + 3) and g(x) = -2|x + 3| + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 5(-1cos(3πx)) = (-2x - 2)/(-2x - 3) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3|(-1sin(2πx + 2) + 2) - 3| + 3 and g(x) = 3|x + 1| - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2(-3cos(3πx - 1) - 3)^2 + 1(-3cos(3πx - 1) - 3) - 4 and g(x) = 3x^2 + 2x - 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2(3cos(2πx - 2) - 2)^2 - 2(3cos(2πx - 2) - 2) - 3 and g(x) = -3x^2 + 3x - 5 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2sin(3π(-2x^2 + 1x - 3) + 3) - 1 = -2x^2 + 4x + 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2cos(2π((-2x + 1)/(-2x + 3)) + 1) and g(x) = (1x + 1)/(2x) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (2(2cos(1πx) - 1) + 1)/(1(2cos(1πx) - 1) + 1) = 5x^2 + 3x + 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1(1cos(2πx + 1) + 2)^2 + 2(1cos(2πx + 1) + 2) + 1 and g(x) = 1|x| + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2cos(2π(-1|x + 1| + 2) - 2) - 3 and g(x) = -1|x - 1| intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1cos(2π(-5x) + 2) - 3 and g(x) = 1x - 4 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2sin(3π((1x - 1)/(1x)) + 2) = 4x^2 + 5x + 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1sin(2π(-5x - 5) + 1) and g(x) = (-2x - 2)/(2x + 1) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3|(2cos(3πx + 3)) - 1| and g(x) = 1|x - 1| - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2|(-2sin(1πx + 3)) - 2| + 2 = (-3x + 3)/(-2x - 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3(3x^2 - 5x - 5)^2 + 5(3x^2 - 5x - 5) and g(x) = 4x^2 - 1x + 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -5(-2sin(3πx + 3) + 2) - 4 and g(x) = -3x - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3cos(1π(-3x^2 - 4x - 3) - 3) - 3 = (1x - 3)/(-2x + 3) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2cos(2π((1x + 1)/(1x)) - 2) + 1 and g(x) = (2x + 3)/(-3x) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2sin(1π(2x^2 + 1x - 1) + 1) = -2|x + 3| - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1(-3sin(1πx - 1) + 3)^2 - 2(-3sin(1πx - 1) + 3) - 5 and g(x) = 1|x + 1| - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2sin(2π(-3x^2 - 4x) + 1) + 2 and g(x) = 2|x + 1| + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1sin(1π(-1x^2 - 3) + 1) - 2 and g(x) = -1|x - 1| + 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1sin(3π((-1x + 1)/(3x - 1)) - 3) + 3 and g(x) = -5x^2 + 3x + 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3(-1cos(3πx + 3) + 1) - 2 and g(x) = -1|x - 3| + 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2sin(3π(-1x^2 - 2x + 5) - 1) and g(x) = -1|x| - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1(3|x - 2| - 2)^2 + 2(3|x - 2| - 2) + 3 and g(x) = (-3x + 1)/(1x + 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-1(2|x| - 2) - 1)/(3(2|x| - 2)) and g(x) = -4x^2 + 2x + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2((-1x + 1)/(-1x + 3))^2 + 5 and g(x) = 3x^2 - 3x + 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-1(-3sin(3πx + 3) + 2) + 2)/(1(-3sin(3πx + 3) + 2) + 1) = (3x + 2)/(-2x + 3) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3|(-3sin(3πx + 2) - 3) - 1| - 2 and g(x) = -5x - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-2(-2cos(2πx + 3)))/(-3(-2cos(2πx + 3)) - 2) and g(x) = 3x + 4 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -5(-2sin(3πx - 3) + 2)^2 + 5(-2sin(3πx - 3) + 2) = 1x^2 - 4x have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3sin(1π(5x^2 + 3x + 3)) - 2 and g(x) = -1x^2 - 3x + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3cos(2π(3|x - 1| + 3) + 2) - 1 and g(x) = (-2x + 1)/(3x + 1) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1|(1sin(3πx) + 3) - 3| - 1 and g(x) = -4x^2 - 2x where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2cos(1π((1x - 2)/(-3x + 2)) + 3) and g(x) = (3x + 2)/(3x + 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3(1sin(2πx - 3) + 1)^2 + 2(1sin(2πx - 3) + 1) - 3 and g(x) = -1x + 4 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -5(2sin(3πx - 1) - 3)^2 - 4(2sin(3πx - 1) - 3) + 2 and g(x) = -3x^2 + 4 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2cos(2π(2x^2 - 1x - 1) - 3) - 2 and g(x) = -1x^2 - 1x - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1(-2sin(1πx + 1) + 1)^2 - 1(-2sin(1πx + 1) + 1) + 2 and g(x) = (-3x + 1)/(2x - 1) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3(1sin(3πx + 2) + 3) - 2 and g(x) = 4x^2 + 5x - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1sin(1π((-2x - 3)/(1x - 3)) + 2) + 1 and g(x) = -1x^2 + 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-2(2cos(2πx - 2)) + 3)/(-1(2cos(2πx - 2)) + 2) = 1|x + 2| - 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1cos(3π((-2x - 3)/(2x - 1)) - 1) - 3 = (2x)/(1x - 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1sin(3π((-1x - 2)/(-3x - 1)) - 1) and g(x) = -1x^2 - 2x where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2cos(3π(4x + 2) + 3) + 3 and g(x) = 4x - 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -4(2cos(2πx + 1) - 2) - 3 = 1x^2 - 1x + 4 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2(-3sin(1πx - 2) - 1) - 4 and g(x) = -3|x - 3| + 2 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -4(-2cos(2πx + 1) - 2) - 5 and g(x) = -3x^2 + 3x + 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1|(2sin(3πx - 2) - 3) + 3| + 2 and g(x) = 3|x| - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3sin(3π(4x)) + 1 and g(x) = -1|x + 1| - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-2(2x^2 + 5x - 5) - 3)/(1(2x^2 + 5x - 5)) and g(x) = 3x^2 - 5x - 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 5(1cos(1πx - 3)) + 1 and g(x) = -3x + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1cos(2π(3x^2 + 1x + 2) + 1) - 2 and g(x) = 3x + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2cos(3π(-1|x - 3| - 3) + 3) + 1 and g(x) = -1|x - 1| in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3(-2sin(2πx + 2) + 3)^2 + 2(-2sin(2πx + 2) + 3) - 2 and g(x) = -5x - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3cos(2π(-3|x - 3| - 3) + 3) - 1 and g(x) = -2|x| - 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -4(-2sin(3πx + 1) - 1) - 1 and g(x) = 3x^2 + 1x + 4 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3cos(1π(2x^2 - 3x + 3) - 2) + 1 and g(x) = (3x)/(-2x - 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2sin(2π(-1|x + 3| - 3) + 2) + 3 and g(x) = (-1x + 3)/(-3x - 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (1(3sin(2πx - 3) - 2) - 3)/(1(3sin(2πx - 3) - 2) + 3) and g(x) = (-1x + 3)/(1x + 1) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3sin(2π(1x^2 - 3x + 4) + 2) - 3 and g(x) = 2x in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (1(-2sin(3πx - 2) - 3) - 2)/(2(-2sin(3πx - 2) - 3)) and g(x) = 1|x| - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1sin(2π(5x + 3) + 3) - 2 and g(x) = -5x^2 - 2x - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3cos(2π(1x^2 - 5x) - 2) + 2 = (-3x + 1)/(2x - 3) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1sin(2π(4x + 4) - 1) - 3 and g(x) = 3|x - 1| - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3(3sin(1πx + 1) + 1) - 3 and g(x) = (-1x + 3)/(-2x - 3) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -1(-2sin(2πx - 2) - 2) + 1 and g(x) = 2|x - 2| - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 2sin(3π((3x)/(-3x - 3)) - 1) - 1 and g(x) = 1x - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2(3cos(3πx - 1) + 2) + 1 and g(x) = 1x^2 + 3x + 4 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 5(-3cos(3πx + 3)) and g(x) = -1x + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2|(3cos(1πx + 1)) + 1| + 2 and g(x) = (2x + 1)/(2x + 1) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 1cos(2π(3x^2 + 1x - 1) - 2) and g(x) = -3x - 5 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (-3(3sin(3πx) - 2) - 1)/(-1(3sin(3πx) - 2) + 2) = (-1x - 2)/(1x + 1) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2sin(2π(5x - 4)) + 1 = 1x^2 + 5x + 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3sin(2π((1x + 2)/(3x + 3)) - 2) and g(x) = 1|x + 2| + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -5(2sin(1πx - 3) + 1) + 3 and g(x) = (3x - 3)/(-2x + 1) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 2(3sin(3πx + 1))^2 - 2(3sin(3πx + 1)) + 3 and g(x) = -1x + 1 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 1(1sin(3πx - 2) - 3)^2 + 1(1sin(3πx - 2) - 3) + 1 = 2|x + 2| - 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1cos(2π(-3|x + 3| - 3) - 3) + 2 and g(x) = 1x - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1|(-2cos(3πx) + 1)| - 2 = -5x^2 - 1x - 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = (-3(2sin(1πx + 2) - 2))/(-1(2sin(1πx + 2) - 2) - 3) and g(x) = 1x - 4 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 1|(3sin(3πx + 2) + 3) - 1| + 2 and g(x) = 4x^2 - 2x + 3 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3(-3sin(1πx - 1) + 2)^2 - 1(-3sin(1πx - 1) + 2) - 1 and g(x) = (3x)/(-1x + 2) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -4(-2cos(3πx + 2) - 1)^2 + 1(-2cos(3πx + 2) - 1) - 1 and g(x) = 4x^2 - 2x - 2 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1(1cos(2πx + 1) - 3)^2 + 1(1cos(2πx + 1) - 3) - 2 and g(x) = 5x - 4 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -2cos(3π(-3|x + 2| + 2) + 1) - 1 and g(x) = -3x where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -3sin(3π(-2|x - 2| - 2) - 3) - 1 and g(x) = -4x^2 + 1x + 4 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 3sin(2π((-3x - 3)/(-3x + 2)) + 3) - 1 and g(x) = -2x^2 + 5x - 3 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2|(-1x^2 + 4x + 3) - 1| + 2 and g(x) = -1x - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2sin(3π(2x + 3) + 2) = (-1x + 2)/(1x + 3) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2cos(3π(1x^2 - 4x - 2) - 1) + 1 = 1x^2 - 1x + 2 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1sin(3π(1x^2)) + 2 and g(x) = -1x where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -1sin(3π(1x^2 + 3x + 2) + 3) + 3 = (3x + 1)/(3x - 2) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -1cos(1π(2|x + 1| - 1) - 2) - 2 and g(x) = (3x - 1)/(-1x - 3) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2cos(1π(-3x + 5) + 2) + 1 and g(x) = (-1x - 2)/(2x + 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2sin(2π(1|x - 2|)) - 1 = (1x + 1)/(-1x - 3) have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2(2sin(1πx - 2) + 2)^2 - 4(2sin(1πx - 2) + 2) + 2 and g(x) = (-2x - 2)/(-2x) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3|(3sin(3πx + 3) + 3) - 1| + 3 and g(x) = -5x^2 + 5x + 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (3(-1cos(3πx - 3) + 2) + 3)/(-1(-1cos(3πx - 3) + 2)) and g(x) = -1x^2 + 5x - 4 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -5(2x^2 + 4x - 1)^2 - 2(2x^2 + 4x - 1) + 1 and g(x) = -1|x - 3| - 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = (-1(-3sin(2πx + 3) + 2) - 3)/(1(-3sin(2πx + 3) + 2)) and g(x) = 3x^2 - 2x + 4 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -1sin(1π(4x^2 - 5x - 1) - 3) - 1 and g(x) = -1x + 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = 4(-2sin(1πx - 1) - 2) - 4 and g(x) = -3|x + 3| - 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -4(2sin(1πx - 3) - 1) - 1 and g(x) = 2|x - 1| + 1 intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3(-1sin(1πx + 3) + 2)^2 - 3(-1sin(1πx + 3) + 2) - 3 and g(x) = (3x - 2)/(-1x - 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3sin(1π((-1x - 2)/(1x)) - 2) - 2 = 1x^2 + 5x - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (3(-2sin(3πx) - 1) + 3)/(-1(-2sin(3πx) - 1) + 2) = 1x^2 - 5x - 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2(3sin(3πx + 2)) + 5 = 1x^2 - 2x + 5 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -3cos(1π(2x - 4) - 3) and g(x) = 2x^2 - 3x + 1 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation (1(-5x^2 - 4x - 1) + 1)/(2(-5x^2 - 4x - 1) + 1) = 3x^2 - 3x + 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = 3sin(1π(-4x^2 - 1x + 1) + 1) + 3 and g(x) = 3|x - 3| where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 5(3cos(1πx + 2) + 1)^2 - 3(3cos(1πx + 2) + 1) + 1 and g(x) = 1x^2 - 2x - 2 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Find the number of times the graphs of f(x) = -2cos(3π((-3x)/(3x + 2)) + 1) - 1 and g(x) = (3x + 3)/(-3x - 2) intersect in the interval [-10, 10].

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation 2(-2cos(2πx + 2))^2 + 5(-2cos(2πx + 2)) - 2 = 1|x - 3| - 3 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 3sin(2π(3x + 3) + 3) and g(x) = 1x + 3 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3cos(1π(-2x^2 + 3x + 1) - 1) + 3 and g(x) = -4x - 4 where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -3sin(1π(-1x - 4) + 3) + 1 = 3|x - 2| - 1 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}


[User]
Determine the number of intersection points between the functions f(x) = -3sin(1π(-4x^2 - 1) + 2) - 2 and g(x) = (-1x - 2)/(-1x - 3) where -10 ≤ x ≤ 10.

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = 2sin(3π(3|x - 2| + 1)) - 1 and g(x) = 1x + 4 in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many points of intersection exist between the functions f(x) = -2|(2|x + 3| - 2) + 1| + 1 and g(x) = (-2x - 1)/(-2x + 3) in the range -10 ≤ x ≤ 10?

Present the answer in LaTex format: \boxed{Your answer}


[User]
How many solutions does the equation -2(-3cos(1πx + 3) - 2) + 5 = 4x^2 + 5 have for x in the interval [-10, 10]?

Present the answer in LaTex format: \boxed{Your answer}