messages listlengths 1 1 | ground_truth stringlengths 1 4 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "How many zeros does the function f(x) = 2|(1|(-3|x| - 1) - 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) = 2|((-2(1x^2 + 5x - 3) - 3)/(-3(1x^2 + 5x - 3) - 1)) - 1| - 2 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) = 2|(2(3sin(2πx - 1)) - 5) - 1| - 3 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) = -3cos(2π(-2|(2|x - 2| + 3) - 1| + 2) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2cos(3π(1(-1x^2 - 1) + 4) + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 600 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-2(1|x - 1| - 3)^2 + 4))/(-2(-2(1|x - 1| - 3)^2 + 4) + 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((3(-3cos(3πx) + 3))/(2(-3cos(3πx) + 3) + 3)))/(3((3(-3cos(3πx) + 3))/(2(-3cos(3πx) + 3) + 3)) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "How many solutions does the equation -5(-2sin(2π(-1x - 1) + 3) + 2)^2 + 1(-2sin(2π(-1x - 1) + 3) + 2) + 4 = 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((-3(2|x + 1| - 1))/(-3(2|x + 1| - 1) - 2))^2 - 3((-3(2|x + 1| - 1))/(-3(2|x + 1| - 1) - 2)) + 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 2(-3|(-1|x + 3| + 2) + 2| + 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 solutions does the equation -3sin(3π(5((2x - 2)/(2x + 2)) - 5)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 191 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1|(-3sin(2π((-2x)/(-3x + 4)) - 1)) + 2| - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 44 | MATH |
[
{
"content": "How many solutions does the equation -5(-3sin(2π((3x + 1)/(2x)) + 1) - 2) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 31 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(2π(-2|((1x - 3)/(1x + 1)) - 2| - 3) + 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 143 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2(3|(2x^2 + 2x - 3) + 1| - 1)^2 + 5(3|(2x^2 + 2x - 3) + 1| - 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(-1cos(2π(5x^2 - 1x - 3) + 1) + 3)^2 - 5(-1cos(2π(5x^2 - 1x - 3) + 1) + 3) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1353 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2(-3sin(3π(-1x^2 + 5x - 5) - 1) - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 289 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(1cos(3π((-3x + 2)/(-2x - 2)) - 3) + 1) + 2)/(2(1cos(3π((-3x + 2)/(-2x - 2)) - 3) + 1) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 81 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2|(3cos(3π(-2|x - 3| + 3) - 3) - 2) + 3| where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 59 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3|(-5(-4x + 1)^2 - 3(-4x + 1) - 2) + 2| - 1 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) = -1cos(1π(-1(5x^2 + 5x + 5)^2 + 1) - 3) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1251 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (1(-2(-3sin(2πx + 2) + 2) - 1) - 1)/(3(-2(-3sin(2πx + 2) + 2) - 1) - 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) = 2cos(3π(1((-1x + 1)/(1x + 2))^2 + 3((-1x + 1)/(1x + 2)))) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 192 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(1π((2(-1x + 1) - 3)/(3(-1x + 1) - 2)) + 1) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 17 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(-4(2cos(3πx + 2) - 1)^2 + 3(2cos(3πx + 2) - 1) + 5) + 4 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(5(-1x^2 + 3x + 2)^2 - 3(-1x^2 + 3x + 2) - 5) - 3)/(-2(5(-1x^2 + 3x + 2)^2 - 3(-1x^2 + 3x + 2) - 5) - 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) = -3|(1(-1cos(1πx + 2) - 3) + 4) - 1| + 2 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) = -3cos(2π(-5(3|x - 2| - 3)^2 - 5(3|x - 2| - 3) + 4) - 2) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1506 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3cos(3π(-2|(1x + 2) + 2| - 1) - 1) + 1 have in the interval [-10, 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) = 1sin(1π(2(1|x - 3| - 1) + 5) + 1) + 1 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) = 3cos(2π(1|(-3x + 2) - 3| + 1) - 1) - 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) = 3sin(2π(-1|(3x - 3) - 1| + 1) - 2) + 2 have in the interval [-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) = -3cos(1π(-5(-3|x + 1| - 1) - 2) + 1) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 146 | MATH |
[
{
"content": "How many solutions does the equation 3sin(1π((3(2x - 5) - 3)/(2(2x - 5) + 3)) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "How many solutions does the equation -2|(2sin(3π((-1x - 1)/(-3x)) + 1) + 1) + 1| + 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) = -1(-2cos(3π((-2x + 3)/(1x)) - 1) + 3) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 107 | MATH |
[
{
"content": "How many solutions does the equation -2sin(3π(3(-3|x - 2| + 2) + 3) + 3) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 266 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3sin(2π(1(-2x^2 - 4x + 3) - 1)) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 357 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1sin(1π(5(-1x - 4) + 1)) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 50 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2|(3|((2x)/(-1x - 3)) + 2| - 2) - 3| + 1 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) = 2|(3sin(2π(4x + 1) - 1) - 1) - 1| - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 320 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3(-1sin(3π(4x^2 - 3x + 5) + 1) - 2)^2 + 2(-1sin(3π(4x^2 - 3x + 5) + 1) - 2) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1132 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1(3cos(3π(3|x - 1| - 3) - 3) + 3)^2 + 1(3cos(3π(3|x - 1| - 3) - 3) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -1(-1(3x^2 - 5x - 4)^2 + 2(3x^2 - 5x - 4) + 1)^2 - 3(-1(3x^2 - 5x - 4)^2 + 2(3x^2 - 5x - 4) + 1) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many solutions does the equation 2(-1(2cos(2πx - 2) - 1)^2 - 5(2cos(2πx - 2) - 1) - 1)^2 + 1(-1(2cos(2πx - 2) - 1)^2 - 5(2cos(2πx - 2) - 1) - 1) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3sin(2π(-4(-1x^2 + 4x + 2)^2 + 3(-1x^2 + 4x + 2) + 1) + 3) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1167 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(1π(1(1x^2 + 3x + 4)^2 - 5(1x^2 + 3x + 4) - 5) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1288 | MATH |
[
{
"content": "How many solutions does the equation -4(1(2|x| - 1)^2 + 5(2|x| - 1) + 3)^2 + 1(1(2|x| - 1)^2 + 5(2|x| - 1) + 3) + 2 = 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) = -2|(-3cos(2π(5x + 5) + 1) + 1)| + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 400 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1sin(3π(-2(-1x - 5)^2 - 2(-1x - 5) + 1) + 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 632 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3cos(3π((2(1x^2 - 5x + 2) + 3)/(1(1x^2 - 5x + 2) + 1)) - 1) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "How many solutions does the equation 2sin(2π(-5(4x + 3)^2 - 1(4x + 3) - 1) + 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1445 | MATH |
[
{
"content": "How many zeros does the function f(x) = -1(3(2cos(2πx)) + 3)^2 - 5(3(2cos(2πx)) + 3) + 2 have in the interval [-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) = -1cos(3π(4(1|x - 2|) + 1) - 1) have in the interval [-10, 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) = (3(5(1x^2 + 3x - 4)^2 + 1(1x^2 + 3x - 4) - 5) + 1)/(-1(5(1x^2 + 3x - 4)^2 + 1(1x^2 + 3x - 4) - 5) - 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) = -1(1cos(3π(1x^2 + 4x + 1) - 3) - 1)^2 + 4(1cos(3π(1x^2 + 4x + 1) - 3) - 1) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 624 | MATH |
[
{
"content": "How many solutions does the equation 2sin(3π(-4(-5x^2 + 3x)^2 + 3(-5x^2 + 3x) - 1) + 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 527 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(1π(-4((-1x + 3)/(1x))^2 + 3((-1x + 3)/(1x)) + 5) + 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 154 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2cos(2π(-2(4x^2 - 3x + 4)^2 + 1(4x^2 - 3x + 4) - 5) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1347 | MATH |
[
{
"content": "How many solutions does the equation 1sin(2π(2((2x - 1)/(-2x + 3)) + 2) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 76 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 1cos(2π(-2|((2x)/(-3x + 2)) + 2| - 3)) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3|(-5(2|x| - 3) + 5)| - 2 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) = 2sin(1π(3(-2x^2 - 2x + 4) - 5) - 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 530 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(3π(1((1x + 3)/(3x - 2))^2 + 2((1x + 3)/(3x - 2)) - 5) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 124 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1|(1((-1x)/(-1x + 2))^2 - 5) + 1| + 2 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) = -2cos(3π(2|(-1x - 3) + 3| + 3) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "How many solutions does the equation 2(2sin(3π(3x^2 - 5x) - 2) - 1) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1389 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3cos(1π(-4(-3x - 4) - 3) + 1) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 119 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2sin(3π(3(-1x^2 + 4x - 1) - 5) + 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1356 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3e^(-1(3|(-1x^2 - 5x) - 3| - 3)) + 2 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 1sin(2π((-2((3x - 1)/(1x)))/(-3((3x - 1)/(1x)) - 1)) + 3) = 0 have in the range [-10, 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) = -2(3sin(2π(-1|x - 3| + 2) + 3) - 3)^2 + 4(3sin(2π(-1|x - 3| + 2) + 3) - 3) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40 | MATH |
[
{
"content": "How many solutions does the equation -1|(1(-2cos(3πx))^2 - 5(-2cos(3πx)) - 4) + 1| + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "How many solutions does the equation 1(-4(2|x| - 3)^2 + 1(2|x| - 3) + 3)^2 - 4(-4(2|x| - 3)^2 + 1(2|x| - 3) + 3) - 4 = 0 have in the range [-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) = (1(-3(2sin(1πx - 2)) - 2))/(3(-3(2sin(1πx - 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) = 2((-1(-1x^2 + 3x + 5) + 1)/(-1(-1x^2 + 3x + 5) - 2))^2 + 2((-1(-1x^2 + 3x + 5) + 1)/(-1(-1x^2 + 3x + 5) - 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) = 2|(2|(-1x^2 + 2x + 4) - 3| - 1) - 3| - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (1(1cos(1π((3x)/(2x - 1)) + 3) - 2) + 2)/(1(1cos(1π((3x)/(2x - 1)) + 3) - 2) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2cos(1π(3|(-4x^2 + 5x + 3) + 3| + 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1577 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(3π(2(-5x^2 + 4x - 5)^2 - 5(-5x^2 + 4x - 5) - 2) + 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 648 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = (-2((3(3sin(1πx) + 2))/(1(3sin(1πx) + 2) - 2)) - 2)/(2((3(3sin(1πx) + 2))/(1(3sin(1πx) + 2) - 2)) - 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((-3(-2sin(3πx - 2) - 1) - 2)/(2(-2sin(3πx - 2) - 1))) - 1)/(-2((-3(-2sin(3πx - 2) - 1) - 2)/(2(-2sin(3πx - 2) - 1))) - 2) 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) = (-1(3cos(3π(-2|x - 1| + 1) + 2) + 2) + 3)/(2(3cos(3π(-2|x - 1| + 1) + 2) + 2) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 119 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 5(-2(2sin(3πx + 1) + 3)^2 + 2(2sin(3πx + 1) + 3) + 4) - 3 equals zero.\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) = 1(2|(5x^2 + 1x - 2) - 2| - 2)^2 + 5(2|(5x^2 + 1x - 2) - 2| - 2) + 2 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) = 1(-3sin(2π(-5x + 4) + 1) + 1)^2 + 1(-3sin(2π(-5x + 4) + 1) + 1) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 200 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(-1|(1sin(2πx) - 3) - 1| + 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) = -5(-1(-2sin(1πx - 3) + 1)^2 - 5(-2sin(1πx - 3) + 1) + 5)^2 - 2(-1(-2sin(1πx - 3) + 1)^2 - 5(-2sin(1πx - 3) + 1) + 5) + 2 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) = 4(3sin(1π(5x + 5) + 3) + 2)^2 + 4(3sin(1π(5x + 5) + 3) + 2) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1sin(1π(3(3|x| - 3) - 4) + 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 90 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2cos(3π(-1|(-1x^2 + 1) - 2| + 1) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 600 | MATH |
[
{
"content": "How many solutions does the equation 2|((-1(1|x + 1| - 3) - 2)/(2(1|x + 1| - 3) + 1)) + 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 zeros does the function f(x) = -4(-2cos(1π(-1x + 5) - 2) - 2)^2 - 5(-2cos(1π(-1x + 5) - 2) - 2) + 4 have in the interval [-10, 10]?\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) = -2(2|(3x^2 - 2x - 1) - 3| + 3)^2 + 5(2|(3x^2 - 2x - 1) - 3| + 3) + 5 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) = -3|(3|(-1x - 5) + 2| - 3)| + 1 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) = -3sin(3π(2|(1|x - 1| + 3) - 2| + 1) - 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 120 | MATH |
[
{
"content": "How many solutions does the equation -3(-1(3sin(3πx - 2) - 1) - 1) - 3 = 0 have in the range [-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) = 4(-1|(-2x^2 - 1x + 4) - 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) = 3(3sin(3π(-4x^2 + 4x - 2)) + 3) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1278 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (2(4(2cos(3πx + 3)) - 3) + 3)/(-3(4(2cos(3πx + 3)) - 3)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 60 | MATH |
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