messages listlengths 1 1 | ground_truth stringlengths 1 4 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "How many zeros does the function f(x) = -2cos(3π(-3x + 3) - 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 90 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2|(3x^2 - 2x + 1) - 2| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (2(-3|(1x + 3) + 3| + 2) + 2)/(-1(-3|(1x + 3) + 3| + 2)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many solutions does the equation -4(1sin(2π(2|((2x)/(-2x + 1))|) + 1)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 53 | MATH |
[
{
"content": "How many solutions does the equation 1|((1(-3x^2 + 2x + 4) - 3)/(2(-3x^2 + 2x + 4) + 1)) + 1| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2|(-1((2(3sin(3πx - 1) - 2) + 1)/(-2(3sin(3πx - 1) - 2) - 3)) - 5) + 3| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3(-2|((-1x)/(-2x + 3)) - 3| - 1)^2 + 2(-2|((-1x)/(-2x + 3)) - 3| - 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many solutions does the equation 4((2(-2cos(2π(1x^2 + 3x - 2)) + 2) - 3)/(-3(-2cos(2π(1x^2 + 3x - 2)) + 2) + 4)) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 75 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3e^(2(-1|x - 2| + 2)) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1|(-2(5((1x + 1)/(2x - 3))^2 + 2((1x + 1)/(2x - 3)) - 5) + 5) - 2| - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(3π((-3x - 1)/(-1x + 2)) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 165 | MATH |
[
{
"content": "How many solutions does the equation -1((-2(-1e^(-2x) + 1) - 1)/(1(-1e^(-2x) + 1)))^2 + 5((-2(-1e^(-2x) + 1) - 1)/(1(-1e^(-2x) + 1))) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3cos(2π(-5x^2 - 3x - 3) - 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1273 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(1π(-3|(3x^2 - 2x - 2) + 1| + 1) + 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 764 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1sin(3π((2(-3(2|x|) + 5))/(-1(-3(2|x|) + 5) - 2)) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 56 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2(-1((1(-1|x + 2| - 1))/(-2(-1|x + 2| - 1) - 1))^2 + 5((1(-1|x + 2| - 1))/(-2(-1|x + 2| - 1) - 1)) + 1) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (1(-1x^2 + 2) - 1)/(-3(-1x^2 + 2) + 4) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(1π(2x + 2) + 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1cos(1π(2|(-3x + 3) - 3| + 1) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3cos(3π((-2x + 3)/(-3x + 4)) + 1) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2|(3sin(1π(5(1x - 1)^2 - 2(1x - 1) + 4) + 1) + 1)| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1385 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3((-3(3cos(1π(1x) + 1) + 3))/(-2(3cos(1π(1x) + 1) + 3) + 1))^2 + 2((-3(3cos(1π(1x) + 1) + 3))/(-2(3cos(1π(1x) + 1) + 3) + 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "How many solutions does the equation -2((-1(2x^2 + 2x - 4) - 3)/(-2(2x^2 + 2x - 4) + 3)) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(2sin(1π((3(1x - 5) - 1)/(-2(1x - 5) - 1)) + 2) - 1)^2 - 5(2sin(1π((3(1x - 5) - 1)/(-2(1x - 5) - 1)) + 2) - 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 34 | MATH |
[
{
"content": "How many solutions does the equation -4(2(1|(1sin(2πx - 1) - 2) - 1| - 2) - 4)^2 + 5(2(1|(1sin(2πx - 1) - 2) - 1| - 2) - 4) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many solutions does the equation 1((-2(-1|x - 3| + 3))/(3(-1|x - 3| + 3) - 2)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2|((1x - 3)/(-2x + 3)) - 1| + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many solutions does the equation (2(-1(3x^2 - 2x) + 2) + 3)/(1(-1(3x^2 - 2x) + 2)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3|(-3e^(-1x) + 1) + 2| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2(-1|x + 3|)^2 + 4(-1|x + 3|) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3cos(3π(-3|x - 1|) - 1) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "How many zeros does the function f(x) = -4(-2cos(2π(-5((-2x - 1)/(-1x - 3))^2 + 2((-2x - 1)/(-1x - 3)) + 5) - 2) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 406 | MATH |
[
{
"content": "How many solutions does the equation 1|(3(3x + 3)^2 - 2(3x + 3)) - 3| - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation -4(-1x^2 + 2x) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2sin(1π((-3x + 3)/(1x - 2)) + 3) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many solutions does the equation -3((1(-5x + 2))/(2(-5x + 2) - 1))^2 - 2((1(-5x + 2))/(2(-5x + 2) - 1)) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(2sin(2π((-1(-3x - 1) - 1)/(2(-3x - 1) - 1)) + 1) - 2) + 1| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1|(2e^(2(-1x^2 + 2x + 2)) - 2) - 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation 1((3(-1(-2|x + 3| + 1)^2 - 4(-2|x + 3| + 1) + 3) - 3)/(-1(-1(-2|x + 3| + 1)^2 - 4(-2|x + 3| + 1) + 3) - 1)) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many solutions does the equation 4(2(2|x| - 2))^2 - 4(2(2|x| - 2)) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2((2(1|(-4x^2 + 5x - 5) + 2| - 1))/(-2(1|(-4x^2 + 5x - 5) + 2| - 1) - 2)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(2|(-1cos(2πx) + 1)| - 2)^2 - 3(2|(-1cos(2πx) + 1)| - 2) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2((2(-5(3|x + 3| - 2)^2 + 4(3|x + 3| - 2) + 1) - 2)/(-2(-5(3|x + 3| - 2)^2 + 4(3|x + 3| - 2) + 1) + 1)) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 4(3(3|((1x + 2)/(1x + 3)) + 2|)^2 + 4(3|((1x + 2)/(1x + 3)) + 2|) - 4) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2(3|((-2(-1x - 5) - 3)/(2(-1x - 5) + 1)) + 3| - 1)^2 + 3(3|((-2(-1x - 5) - 3)/(2(-1x - 5) + 1)) + 3| - 1) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3 | MATH |
[
{
"content": "How many solutions does the equation -1(2|((3(-3x - 5) + 1)/(-2(-3x - 5) + 3)) + 1| + 1)^2 + 3(2|((3(-3x - 5) + 1)/(-2(-3x - 5) + 3)) + 1| + 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1sin(3π(-1|((-3(2x + 2) + 2)/(1(2x + 2)))| - 3) - 3) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3sin(3π(-1|((2x + 3)/(3x + 3)) + 1| - 2) + 2) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 35 | MATH |
[
{
"content": "How many zeros does the function f(x) = -5(-2x^2 + 3x + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many solutions does the equation 3((-2(-1x^2 + 2x + 1) - 3)/(3(-1x^2 + 2x + 1) + 3)) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3(2(1|((3x)/(-2x - 1)) + 3| - 2)^2 - 5(1|((3x)/(-2x - 1)) + 3| - 2) + 3) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (3(3cos(3π(1x^2 + 3x - 3) + 3)) + 2)/(1(3cos(3π(1x^2 + 3x - 3) + 3)) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 614 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(1x^2 - 4x + 4) - 1| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3((3(-5(-2|x - 3| - 1) - 5) - 1)/(-1(-5(-2|x - 3| - 1) - 5) + 3))^2 + 2((3(-5(-2|x - 3| - 1) - 5) - 1)/(-1(-5(-2|x - 3| - 1) - 5) + 3)) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
... | 2 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3e^(1(-2x^2 - 2x + 2)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2(-2(-3sin(3πx) - 1)^2 - 5(-3sin(3πx) - 1) + 3) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1(1(-2|((1x + 1)/(-3x + 1)) - 2| + 3)^2 - 3(-2|((1x + 1)/(-3x + 1)) - 2| + 3) - 4) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(3π(-3|(1x^2 + 2) - 1| - 3) - 1) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1254 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(3π((-1x + 3)/(2x + 3)) - 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 89 | MATH |
[
{
"content": "How many solutions does the equation (-1(-5(1x^2 - 3x + 1) + 5) + 3)/(1(-5(1x^2 - 3x + 1) + 5) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(1(4(1e^(-1x) - 1)^2 - 4(1e^(-1x) - 1) - 1)) - 2| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-2(-2(5x^2 + 4x - 4) + 5))/(1(-2(5x^2 + 4x - 4) + 5) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2|(1(3sin(1π(2x + 3) - 1) + 1)^2 - 1) + 2| + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2((2(-2|(-3x + 4) - 1|))/(-1(-2|(-3x + 4) - 1|) - 2))^2 - 2((2(-2|(-3x + 4) - 1|))/(-1(-2|(-3x + 4) - 1|) - 2)) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (1(-2(-1cos(2πx - 2) - 1)^2 - 1(-1cos(2πx - 2) - 1)) + 1)/(-3(-2(-1cos(2πx - 2) - 1)^2 - 1(-1cos(2πx - 2) - 1)) + 4) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many zeros does the function f(x) = (2(-3(2x^2 + 5x + 3) + 4) - 2)/(3(-3(2x^2 + 5x + 3) + 4) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -5(2|((-3(2x^2 - 5x - 5) + 3)/(-2(2x^2 - 5x - 5) + 3)) + 1| - 3) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3sin(3π((3(4(5x - 4)^2 - 5(5x - 4) - 5) + 1)/(3(4(5x - 4)^2 - 5(5x - 4) - 5)))) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 4(3|((1x - 1)/(3x + 3)) + 2| - 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 5(-2(1|((-1x + 3)/(3x + 1)) - 3| - 2)^2 + 2(1|((-1x + 3)/(3x + 1)) - 3| - 2) + 3) + 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many solutions does the equation 4((3x - 1)/(3x - 2))^2 - 4((3x - 1)/(3x - 2)) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1(-3|x - 1|)^2 - 2(-3|x - 1|) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many solutions does the equation (3(-1|x - 3|) + 2)/(1(-1|x - 3|) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2(-1|((-2(4x + 5) - 2)/(-1(4x + 5))) + 3|)^2 + 1(-1|((-2(4x + 5) - 2)/(-1(4x + 5))) + 3|) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (2(2|(-2x^2 + 3x - 1) + 2|) - 1)/(-1(2|(-2x^2 + 3x - 1) + 2|)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(3(-2sin(3π(-1x^2 + 1x) + 2) + 1) - 3) - 1)/(-1(3(-2sin(3π(-1x^2 + 1x) + 2) + 1) - 3) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 585 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (1(4(1|x - 3| - 1)^2 - 5(1|x - 3| - 1)) + 1)/(3(4(1|x - 3| - 1)^2 - 5(1|x - 3| - 1)) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(3π((1x + 1)/(-3x)) + 2) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1(1(2|x + 3| + 2) + 2)^2 - 5(1(2|x + 3| + 2) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2sin(2π(-4(-1x^2 - 4x + 1) - 3) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1311 | MATH |
[
{
"content": "How many solutions does the equation (3(5(-1x^2 - 4x + 3) + 3) - 1)/(-2(5(-1x^2 - 4x + 3) + 3) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 5(-2|x + 1|)^2 - 5(-2|x + 1|) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2cos(1π(-1|(1x + 2) - 2|) + 3) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3(3e^(-2(3((3x + 1)/(2x - 1))^2 - 4((3x + 1)/(2x - 1)) - 2)) - 2) + 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many solutions does the equation 4(2cos(1π(-2|(2x^2 + 4x - 2) + 1| - 1) + 3) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 792 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2cos(3π(-2|(1x^2 + 4x + 4) - 2| + 2) + 3) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 521 | MATH |
[
{
"content": "How many solutions does the equation 3sin(2π(5((2(-2x - 2) + 1)/(-2(-2x - 2) - 2))^2 + 3((2(-2x - 2) + 1)/(-2(-2x - 2) - 2)) + 5) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 69 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3cos(3π(3|(-4x + 3) + 3|) + 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 719 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1(-3|((1x + 3)/(-1x + 2)) - 2| + 1)^2 - 5(-3|((1x + 3)/(-1x + 2)) - 2| + 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(3π(3|(-5x^2 - 2x + 3)| - 3) - 1) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1186 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-2(-1(3|x + 3| - 3)^2 + 4(3|x + 3| - 3) + 2) + 2)/(-3(-1(3|x + 3| - 3)^2 + 4(3|x + 3| - 3) + 2) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (1(1|x - 2| - 1) - 3)/(3(1|x - 2| - 1) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many solutions does the equation -3e^(-2(-1(-1((-3x - 2)/(1x))^2 - 4((-3x - 2)/(1x)) - 3) - 4)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2|((3(2x^2 - 1x - 5) - 1)/(-1(2x^2 - 1x - 5))) - 3| - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-1(4(2sin(2πx + 1) + 2)^2 + 1(2sin(2πx + 1) + 2) - 5) - 3)/(-2(4(2sin(2πx + 1) + 2)^2 + 1(2sin(2πx + 1) + 2) - 5) - 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3|((2(3x^2 - 5x + 1) + 1)/(-1(3x^2 - 5x + 1) + 2)) + 3| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(-3(2|((-2x - 3)/(-2x - 2)) + 2| - 3) + 3)^2 - 2(-3(2|((-2x - 3)/(-2x - 2)) + 2| - 3) + 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3(-4((-1x + 2)/(2x - 3)) + 4)^2 - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3cos(2π(1(1x^2 + 3x - 5) - 4) + 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 408 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2((-2(1|x - 3| - 2) + 3)/(1(1|x - 3| - 2) - 2)) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 | MATH |
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