messages listlengths 1 1 | ground_truth stringlengths 1 4 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3sin(1π(1|((1x - 2)/(1x)) + 2| + 2) - 2) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 49 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(1π(-2|((-3x - 1)/(2x + 2)) + 2| + 3) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 55 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(2π((2(3|x - 2| + 1) - 3)/(-1(3|x - 2| + 1) + 2)) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(-5(-1sin(1πx + 1) + 2) + 4) + 3 have in the interval [-10, 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) = -1cos(3π(-5(1x - 2)^2 + 2(1x - 2) + 4) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1659 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 5((-2(-3sin(3πx - 1) - 1) - 2)/(-1(-3sin(3πx - 1) - 1) + 3)) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2(2|(-1|x + 1| + 3) - 2| + 2) - 5 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) = -3cos(2π(-4(-5x + 2)^2 - 3(-5x + 2) + 1) + 2) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1222 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (1(-1sin(2π(5x^2 - 4x + 4) - 2) - 1) + 2)/(3(-1sin(2π(5x^2 - 4x + 4) - 2) - 1) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 977 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-1(4(-2sin(2πx - 2) + 3)^2 - 2) + 2)/(-3(4(-2sin(2πx - 2) + 3)^2 - 2)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1(-4(-2sin(3πx - 1) + 3)^2 + 5(-2sin(3πx - 1) + 3) + 3) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(3π(-1(5x^2 - 5x + 3)^2 + 5(5x^2 - 5x + 3) + 1) + 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1060 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3cos(1π(5(-3|x - 1| + 3) + 2) + 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 298 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(3π(1|(4x^2 - 2x + 1)|) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1582 | MATH |
[
{
"content": "How many solutions does the equation -1(-2cos(3π(-1|x - 3| + 1) + 3) - 1)^2 + 4(-2cos(3π(-1|x - 3| + 1) + 3) - 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many solutions does the equation -1(3sin(3π(2x^2 - 1) - 1) - 2)^2 + 5(3sin(3π(2x^2 - 1) - 1) - 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1050 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2sin(1π((-1(3x + 3) - 3)/(-2(3x + 3) - 1)) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1((1(-3sin(1πx - 2) + 3) + 1)/(-1(-3sin(1πx - 2) + 3)))^2 - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -5(1(-4x^2 - 4x + 5)^2 + 2(-4x^2 - 4x + 5)) + 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(-5(3cos(2πx - 2) + 2) - 3) + 2)/(-1(-5(3cos(2πx - 2) + 2) - 3) - 2) have in the interval [-10, 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) = 2sin(1π(-5(2x^2 - 4x + 4)^2 - 4(2x^2 - 4x + 4) + 2) - 2) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1280 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2cos(1π(1(-3x^2 - 3x + 2) - 1) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 602 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2|((-2(-2sin(1πx - 3)))/(2(-2sin(1πx - 3)) - 1)) - 3| - 1 equals zero.\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) = -2cos(3π(-2|(2|x - 2| + 3) - 2|) + 2) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-1|(1cos(3πx - 3) + 2) - 1| - 2)^2 + 3(-1|(1cos(3πx - 3) + 2) - 1| - 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-1((2(3cos(1πx + 3) + 3) - 3)/(-3(3cos(1πx + 3) + 3) + 4)) + 1)/(1((2(3cos(1πx + 3) + 3) - 3)/(-3(3cos(1πx + 3) + 3) + 4))) equals zero.\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) = -2sin(3π(-3|(-3|x + 1| + 2) + 3| - 1) - 1) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 540 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2(-2sin(1π((3x + 2)/(3x - 1)) + 1) - 2)^2 + 4(-2sin(1π((3x + 2)/(3x - 1)) + 1) - 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1(2cos(1π(1x^2 + 4x + 3) + 1) + 2)^2 + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 208 | MATH |
[
{
"content": "How many solutions does the equation -3|(2cos(2π(4x - 1) + 2) + 2) - 3| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 101 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2(3(-2x^2 - 5x + 3)^2 + 4(-2x^2 - 5x + 3) + 3) + 5 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) = -2cos(3π(-2|(-4x^2 - 4x + 2) - 3| + 2)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1631 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2(-1(-2cos(2πx + 2) - 3) - 4) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3|(2(-1|x - 2| - 2)^2 + 3(-1|x - 2| - 2) - 5) - 1| + 1 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) = 5(1|(-4x^2 + 3x + 4) + 1| - 2) - 1 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) = 3|(5(2x)^2 + 4(2x)) - 1| - 2 have in the interval [-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) = 2sin(3π(2|(2x^2 + 4x + 2) - 1| + 1) + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 951 | MATH |
[
{
"content": "How many solutions does the equation 4(-2cos(2π(2|x - 1| + 3) - 3) - 1) + 3 = 0 have in the range [-10, 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) = -4(2cos(2π(-3x^2 - 1x - 2) - 2))^2 + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1338 | MATH |
[
{
"content": "How many solutions does the equation 1|(1cos(3π((-2x - 2)/(2x - 1)) + 1)) + 2| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 78 | MATH |
[
{
"content": "How many solutions does the equation 1|(-2|(3sin(2πx + 3)) - 1|) + 2| - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-2((-1(-2cos(2πx - 3)) - 2)/(-3(-2cos(2πx - 3)) + 2)) + 3)/(-3((-1(-2cos(2πx - 3)) - 2)/(-3(-2cos(2πx - 3)) + 2)) + 4) equals zero.\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) = -1(-1|(-5x^2 + 4x + 3) - 2|)^2 + 4(-1|(-5x^2 + 4x + 3) - 2|) + 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) = (3(-2sin(2π(2x^2 - 1x - 3) - 3) - 1) + 2)/(2(-2sin(2π(2x^2 - 1x - 3) - 3) - 1) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 281 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1cos(2π(-5((1x + 3)/(1x - 3)) - 2) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 275 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(1(3sin(1πx) + 3) - 3) + 1)/(-1(1(3sin(1πx) + 3) - 3) - 2) 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) = -3(3sin(1π((1x)/(-3x - 2)) + 2)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16 | MATH |
[
{
"content": "How many solutions does the equation (-1(2cos(2π((-2x - 1)/(-2x - 3)) - 3) - 2) - 2)/(-2(2cos(2π((-2x - 1)/(-2x - 3)) - 3) - 2) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 55 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2(3sin(2π((1x - 1)/(-1x + 2)) + 3) + 3)^2 - 3(3sin(2π((1x - 1)/(-1x + 2)) + 3) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(1π(-3(1x^2 + 1x - 3)^2 - 5(1x^2 + 1x - 3) - 3) - 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1052 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -4(-3sin(3π(1x - 5) + 3) + 3)^2 + 1(-3sin(3π(1x - 5) + 3) + 3) + 4 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 (-2(-4(2sin(1πx - 2))^2 - 4(2sin(1πx - 2)) - 2) - 3)/(1(-4(2sin(1πx - 2))^2 - 4(2sin(1πx - 2)) - 2) - 3) = 0 have in the range [-10, 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(-1(-2cos(2πx - 2) + 3)^2 + 1(-2cos(2πx - 2) + 3) - 1) - 2)/(-1(-1(-2cos(2πx - 2) + 3)^2 + 1(-2cos(2πx - 2) + 3) - 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3|(-1(5x)^2 - 1(5x) + 5)| - 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) = 4(1(3|x - 2| - 1)^2 - 5(3|x - 2| - 1) - 4)^2 - 4(1(3|x - 2| - 1)^2 - 5(3|x - 2| - 1) - 4) 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) = 1(3cos(1π(-1x + 2) - 1) - 2)^2 - 4(3cos(1π(-1x + 2) - 1) - 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1(3sin(2π(5x - 3) + 2) - 2)^2 + 2(3sin(2π(5x - 3) + 2) - 2) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 200 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2sin(1π(1|(1x^2 - 5x - 1) - 2| + 1)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 107 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3sin(3π(2((-3x - 3)/(-2x - 1))^2 - 4((-3x - 3)/(-2x - 1)) - 2)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 89 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3(-4(-5x^2 + 3x + 3)^2 + 4(-5x^2 + 3x + 3) + 2) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2sin(2π(3|(5x^2 - 1x - 2) - 3| - 2) - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 968 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3|(2|(-5x^2 + 1x + 2) - 2| - 1)| + 1 have in the interval [-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) = -1cos(3π(-2(4x + 3)^2 + 4(4x + 3) - 3) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1212 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3sin(1π((1(-4x + 1) + 3)/(3(-4x + 1) - 2)) - 1) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9 | MATH |
[
{
"content": "How many solutions does the equation 2sin(3π((2(-3|x|) - 1)/(3(-3|x|) + 3))) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 43 | MATH |
[
{
"content": "How many solutions does the equation -3cos(2π(-5(2x - 2)^2 + 3(2x - 2) + 2)) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1110 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2|(3cos(2π(3|x + 1| + 1) + 2)) + 2| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 56 | MATH |
[
{
"content": "How many solutions does the equation 5(4(2sin(3πx + 3))^2 - 5(2sin(3πx + 3)) + 1) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2cos(2π(1|(3|x + 3| + 3) - 2|) - 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(-1(1sin(3πx - 3) - 3) - 3)| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -4(3sin(1π(-4x^2 + 2x + 2) - 2) + 3) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 613 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3sin(1π(4(2|x - 2| - 3)^2 - 3(2|x - 2| - 3) + 4) - 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 878 | MATH |
[
{
"content": "How many solutions does the equation -1((2(-1x^2 - 4x + 4) - 2)/(-1(-1x^2 - 4x + 4) - 1))^2 - 2((2(-1x^2 - 4x + 4) - 2)/(-1(-1x^2 - 4x + 4) - 1)) + 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 zeros does the function f(x) = -4(3cos(2π(-4x - 3) + 3) - 1)^2 - 3(3cos(2π(-4x - 3) + 3) - 1) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 320 | MATH |
[
{
"content": "How many solutions does the equation 4(-5(3|x - 3| - 2)^2 - 5(3|x - 3| - 2) + 4) - 3 = 0 have in the range [-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) = -2cos(2π(1|(3x^2 + 2x + 2)| + 2)) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1076 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2|((-3(1x^2 - 2x - 3))/(3(1x^2 - 2x - 3) - 1)) + 3| - 3 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) = -3(3sin(1π((1x - 2)/(-2x - 1)) + 1) + 1) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -5(-2cos(3π(1x - 1) + 2))^2 + 2(-2cos(3π(1x - 1) + 2)) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3(-2(3sin(3πx - 1) + 2) + 1) + 1 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) = -2(1(1|x + 2| - 3) - 1)^2 + 4 have in the interval [-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) = -2cos(2π(-1(3x + 3)^2 - 1(3x + 3) - 2) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1696 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3cos(3π((3(2|x - 3| - 2) - 3)/(2(2|x - 3| - 2) - 1)) + 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 39 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-2(-1cos(3π((-3x)/(2x + 3)) + 2) + 2) + 3)/(2(-1cos(3π((-3x)/(2x + 3)) + 2) + 2) + 1) 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) = 5((-2(2x^2 - 5x - 4) + 1)/(-2(2x^2 - 5x - 4)))^2 - 1((-2(2x^2 - 5x - 4) + 1)/(-2(2x^2 - 5x - 4))) - 5 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) = -1sin(3π(-4(3x + 5)^2 + 2(3x + 5) - 3) - 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1203 | MATH |
[
{
"content": "How many zeros does the function f(x) = -4(5(2|x - 2|)^2 - 1(2|x - 2|) - 4)^2 + 1(5(2|x - 2|)^2 - 1(2|x - 2|) - 4) + 3 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 5(3sin(1π(-2|x - 2| + 3)) - 2) - 1 = 0 have in the range [-10, 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) = (-2(-1|(-5x^2 - 3x + 3) - 1|) - 2)/(1(-1|(-5x^2 - 3x + 3) - 1|)) equals zero.\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) = -2(1(-3cos(2πx + 1) + 1) - 3)^2 + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "How many solutions does the equation 1((2(3sin(2πx + 1) + 1))/(1(3sin(2πx + 1) + 1) - 2)) - 5 = 0 have in the range [-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(3sin(2π(-5x + 3) + 1) + 3)^2 - 4(3sin(2π(-5x + 3) + 1) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 97 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2|((-3(3cos(2πx - 3) - 3))/(2(3cos(2πx - 3) - 3) - 1)) + 2| - 3 equals zero.\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) = 3(-2|(3|x + 1|)| + 2)^2 + 1(-2|(3|x + 1|)| + 2) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4 | MATH |
[
{
"content": "How many zeros does the function f(x) = (-1(4(-2cos(1πx - 3) - 2) + 2) - 1)/(3(4(-2cos(1πx - 3) - 2) + 2) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many zeros does the function f(x) = 4(2(3x^2 + 4x + 3) - 5)^2 - 3(2(3x^2 + 4x + 3) - 5) - 5 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) = -3sin(3π(-3(5x - 5)^2 - 3) - 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1497 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3(-4(2cos(3πx - 1) - 2)^2 + 4(2cos(3πx - 1) - 2) + 5) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
[
{
"content": "How many solutions does the equation -1cos(2π(-2|(-1x^2 - 1x - 4) + 2| + 1)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 362 | MATH |
[
{
"content": "How many zeros does the function f(x) = (3((-3(3sin(2πx + 3) + 2) + 1)/(-1(3sin(2πx + 3) + 2) - 2)) - 3)/(3((-3(3sin(2πx + 3) + 2) + 1)/(-1(3sin(2πx + 3) + 2) - 2)) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
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