messages listlengths 1 1 | ground_truth stringlengths 1 4 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "How many zeros does the function f(x) = -2(-2sin(3π(3|x + 1| + 2) + 3)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 182 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2sin(1π(-2((1x + 2)/(2x - 1))) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 58 | MATH |
[
{
"content": "How many solutions does the equation (-1(4(-2sin(2πx) - 1) - 4) - 1)/(1(4(-2sin(2πx) - 1) - 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) = 2sin(3π(-1|(3x^2 - 1x + 3) + 1|) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1444 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2sin(3π((1((1x + 2)/(-3x + 4)))/(1((1x + 2)/(-3x + 4)) + 2)) - 1) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 57 | MATH |
[
{
"content": "How many zeros does the function f(x) = -4((2(-2cos(1πx - 3) + 1) - 1)/(2(-2cos(1πx - 3) + 1) + 1)) - 5 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) = 3(1|(2|x - 1|) - 1|)^2 + 3(1|(2|x - 1|) - 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) = -1|(-1(-2sin(1πx - 3) - 1) - 1) - 3| + 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) = -3cos(2π(-3((-3x + 2)/(-3x + 1))^2 + 3((-3x + 2)/(-3x + 1)) - 3) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 65 | MATH |
[
{
"content": "How many solutions does the equation -5(3|(-4x^2 + 4) - 3| - 1) - 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) = -2cos(3π((2(2|x| - 3) - 3)/(2(2|x| - 3) - 1)) + 2) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 46 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -3|(-5(-1x + 5)^2 + 4(-1x + 5) + 5) - 2| + 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) = 2sin(3π(1(1x^2 - 3x + 4)^2 - 4(1x^2 - 3x + 4) - 2) - 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1212 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(2π(4(-1|x - 1| - 3) + 1) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2sin(1π(2|((3x + 2)/(1x)) + 2| - 3) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 76 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3(-2|(3|x| + 1) - 2| - 1) - 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) = -4(3|(-5x + 3) - 1| - 2)^2 + 5(3|(-5x + 3) - 1| - 2) + 4 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) = -3cos(2π(-5(5x + 4)^2) - 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1507 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (1(-1sin(3π((-3x - 3)/(-2x + 3)) + 3) + 2) - 1)/(-1(-1sin(3π((-3x - 3)/(-2x + 3)) + 3) + 2) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 72 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3cos(1π(2|(5x - 5) - 1| + 3)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 200 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3|(-1(-2sin(1πx - 3)) + 1)| + 3 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 1|((2(-4x^2 + 3) - 1)/(2(-4x^2 + 3)))| - 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) = 1cos(3π(1(1|x + 2| + 3) - 5) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(3π(3|((2x - 1)/(-1x - 1)) + 1|) + 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 179 | MATH |
[
{
"content": "How many zeros does the function f(x) = -5(-1(-2cos(1πx - 3) - 2)^2 - 5(-2cos(1πx - 3) - 2) - 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many solutions does the equation 2(-3(1x^2 - 1x - 3) + 4)^2 - 4(-3(1x^2 - 1x - 3) + 4) - 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) = 1cos(2π(5(-5x + 2) + 3) - 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 486 | MATH |
[
{
"content": "How many zeros does the function f(x) = 1|(1(-1x^2 + 5x) + 4) + 1| - 2 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((3(-3sin(2πx - 1) + 2) - 3)/(-3(-3sin(2πx - 1) + 2) - 1)) - 1)/(-1((3(-3sin(2πx - 1) + 2) - 3)/(-3(-3sin(2πx - 1) + 2) - 1)) + 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) = -1(-1(1x^2 + 1x - 4)^2 - 1(1x^2 + 1x - 4) + 4)^2 - 3(-1(1x^2 + 1x - 4)^2 - 1(1x^2 + 1x - 4) + 4) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many zeros does the function f(x) = -3cos(2π(-5((2x - 3)/(2x + 3)) - 4) + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 176 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2cos(3π(5(-3x - 3) - 2) + 2) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 423 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2|(1sin(1π(2x + 5) + 3) + 3) - 3| - 2 have in the interval [-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) = -2sin(3π(3|(1x^2 + 4x + 3) + 3| - 1) + 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 769 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = (3(1|(1sin(2πx - 1) + 1) - 3| - 2) - 3)/(2(1|(1sin(2πx - 1) + 1) - 3| - 2) + 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) = -1(-4(1cos(1πx - 3))^2 + 4(1cos(1πx - 3)))^2 + 1 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) = 1sin(3π(-3|((-2x)/(-2x - 1)) + 1| - 1) - 2) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -5((2(3sin(2πx + 3) - 2) - 3)/(-2(3sin(2πx + 3) - 2)))^2 + 2 where -10 ≤ x ≤ 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) = -5(3sin(2π(-3x^2 + 5x + 3) + 1) - 1) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1066 | MATH |
[
{
"content": "How many solutions does the equation 3sin(3π(-4(-5x - 3)^2 - 3(-5x - 3) + 3)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1575 | MATH |
[
{
"content": "How many solutions does the equation -1sin(3π(2(5x + 5)^2 + 1(5x + 5)) + 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1227 | MATH |
[
{
"content": "How many solutions does the equation -2(-2|(-1|x - 3| - 2) + 3| + 3)^2 + 1(-2|(-1|x - 3| - 2) + 3| + 3) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6 | MATH |
[
{
"content": "How many solutions does the equation 1cos(2π(5(2|x|) + 1) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 400 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2sin(2π(5(2|x + 1| - 2)^2 + 1(2|x + 1| - 2) - 4) - 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1015 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3|(-1|(-5x - 1) + 1| + 2) + 3| - 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(3cos(3π(-3x^2 + 3x + 1) - 2) - 1) - 2)/(-1(3cos(3π(-3x^2 + 3x + 1) - 2) - 1) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 856 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1(3(-4x^2 - 2x + 1)^2 - 1(-4x^2 - 2x + 1) + 2) + 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) = -1sin(3π(-4(-3x^2 - 2x + 2)^2 - 5(-3x^2 - 2x + 2) + 1) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1096 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 3(-2((-2x - 1)/(1x + 2))^2 + 4((-2x - 1)/(1x + 2)))^2 + 4(-2((-2x - 1)/(1x + 2))^2 + 4((-2x - 1)/(1x + 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) = (1((1(1cos(3πx - 1) - 1) + 3)/(1(1cos(3πx - 1) - 1) + 1)) + 2)/(2((1(1cos(3πx - 1) - 1) + 3)/(1(1cos(3πx - 1) - 1) + 1)) - 1) 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) = (-1((1(1cos(3πx - 3) + 1) - 2)/(-3(1cos(3πx - 3) + 1) + 4)) + 3)/(1((1(1cos(3πx - 3) + 1) - 2)/(-3(1cos(3πx - 3) + 1) + 4)) + 2) 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(2|(1x - 5) - 2| - 1)^2 + 5(2|(1x - 5) - 2| - 1) - 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) = -4(3sin(1π(4x^2 - 3x - 3) - 3)) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 798 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1cos(3π(4(3|x + 2| + 2) - 5) + 3) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 349 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3sin(3π(2|(2x - 4) + 2| - 1) + 2) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 117 | MATH |
[
{
"content": "How many solutions does the equation -3cos(2π(2(-1x - 1) - 1) - 1) + 1 = 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) = 1|(-2|((3x + 2)/(2x + 3)) + 3| + 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) = 1((-3(-2|x - 3| + 1))/(1(-2|x - 3| + 1) + 1))^2 + 4((-3(-2|x - 3| + 1))/(1(-2|x - 3| + 1) + 1)) - 5 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(2π(-3(-4x - 2)^2 + 5(-4x - 2) + 3) - 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1570 | MATH |
[
{
"content": "How many zeros does the function f(x) = 2|(-2(3x^2 + 5x + 1)^2 + 2(3x^2 + 5x + 1) + 5) - 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many solutions does the equation 1|(2|((1x - 3)/(-3x + 4)) + 1| - 3) - 2| - 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) = 1(2cos(3π(-3x + 4) + 3) - 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 180 | MATH |
[
{
"content": "How many solutions does the equation 2|(3((1x - 1)/(-1x + 2))^2 + 3((1x - 1)/(-1x + 2)) - 2) - 3| - 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 solutions does the equation 1sin(2π((1(-1x - 4) - 1)/(2(-1x - 4) + 2)) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 54 | MATH |
[
{
"content": "How many solutions does the equation (1(2(2x^2 + 2x - 1)^2 - 3(2x^2 + 2x - 1) - 3) - 3)/(1(2(2x^2 + 2x - 1)^2 - 3(2x^2 + 2x - 1) - 3) + 3) = 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|(3cos(3π(-1|x - 3|) + 3) - 3)| + 2 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|(2cos(2πx - 1) + 2) - 1| + 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2|(3cos(3π(-2x - 1) - 2) + 2) - 3| - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 240 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 3(-2cos(2π(-2|x| - 3) - 2) - 3) + 4 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(1x^2 + 4x - 1)^2 + 5(1x^2 + 4x - 1) - 3)^2 + 3(2(1x^2 + 4x - 1)^2 + 5(1x^2 + 4x - 1) - 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 5(3(-1|x + 1| + 2)^2 + 3(-1|x + 1| + 2) - 1)^2 + 2(3(-1|x + 1| + 2)^2 + 3(-1|x + 1| + 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(-2cos(1π((-2x + 3)/(-3x + 4)) - 1) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -1|(1(-1sin(2πx - 3) - 1) + 1) - 1| + 1 where -10 ≤ x ≤ 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) = 5(2cos(2π((-1x + 3)/(-2x + 1)) + 1)) + 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 54 | MATH |
[
{
"content": "How many solutions does the equation -2sin(1π(1(1|x - 2| - 1) - 2) + 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20 | MATH |
[
{
"content": "How many solutions does the equation 2|(5((-2x + 3)/(1x + 3))^2 - 5((-2x + 3)/(1x + 3)) - 1) + 1| - 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) = 1cos(1π(1(3x^2 - 1x - 3)^2 + 2(3x^2 - 1x - 3) + 1) + 3) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1146 | MATH |
[
{
"content": "How many zeros does the function f(x) = 5(-4(2|x + 1| - 3)^2 - 1(2|x + 1| - 3) + 3)^2 - 1(-4(2|x + 1| - 3)^2 - 1(2|x + 1| - 3) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2cos(1π((-1(2x^2 - 3x - 2) + 2)/(2(2x^2 - 3x - 2) + 1)) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 42 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3sin(2π(4(1|x - 2| + 2) + 1) + 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 160 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2|(1cos(3π(-4x + 5)) + 2) - 3| where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 118 | MATH |
[
{
"content": "How many solutions does the equation (-2((-1(3sin(2πx - 2) + 2) + 1)/(-1(3sin(2πx - 2) + 2))))/(-3((-1(3sin(2πx - 2) + 2) + 1)/(-1(3sin(2πx - 2) + 2))) + 4) = 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) = 2cos(2π(3(3|x + 3| - 2) - 3) - 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 360 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(3π(-5((2x + 3)/(-2x - 2))^2 - 1((2x + 3)/(-2x - 2)) - 2)) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 70 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = -2(-2|((1x - 1)/(-3x + 2)) + 1| + 3)^2 + 3(-2|((1x - 1)/(-3x + 2)) + 1| + 3) + 4 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) = (2(-1(-5x^2 + 4x + 4)^2 - 3(-5x^2 + 4x + 4) - 2) + 1)/(-1(-1(-5x^2 + 4x + 4)^2 - 3(-5x^2 + 4x + 4) - 2) + 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((-1(3x^2 - 4x - 1) - 3)/(-1(3x^2 - 4x - 1) + 2)) + 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 62 | MATH |
[
{
"content": "How many solutions does the equation 3cos(3π(4(3|x - 3| + 2) - 4) - 3) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 720 | MATH |
[
{
"content": "How many solutions does the equation (-1(2|(-2sin(3πx - 1) + 2) - 2|) + 1)/(-1(2|(-2sin(3πx - 1) + 2) - 2|) - 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 zeros does the function f(x) = 2(-1sin(1π(-3|x - 1| + 3) + 1) - 3)^2 + 2(-1sin(1π(-3|x - 1| + 3) + 1) - 3) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29 | MATH |
[
{
"content": "Find the number of x-intercepts of the function f(x) = 2(1sin(2π(-4x^2 - 4x - 2) + 2) - 2)^2 + 4(1sin(2π(-4x^2 - 4x - 2) + 2) - 2) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 882 | MATH |
[
{
"content": "Determine the number of values x in [-10, 10] where f(x) = 5(-2cos(3π((-1x + 1)/(-3x - 2)) - 2) - 1)^2 + 2(-2cos(3π((-1x + 1)/(-3x - 2)) - 2) - 1) - 5 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(1|(-5x^2 - 2x + 1) - 2| - 2)^2 + 5(1|(-5x^2 - 2x + 1) - 2| - 2) + 4 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) = 4(-2cos(2π(3x^2 - 3x - 3) - 3) + 1) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1022 | MATH |
[
{
"content": "How many solutions does the equation 1(-3cos(3π(2x^2 + 1x + 1) + 2) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1129 | MATH |
[
{
"content": "How many solutions does the equation 1|(3sin(3π(-3x^2 + 1x + 5) - 1) + 1) + 2| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 753 | MATH |
[
{
"content": "How many zeros does the function f(x) = 3sin(3π((3((-1x + 2)/(-3x + 1)) + 3)/(-2((-1x + 2)/(-3x + 1)) + 3))) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 49 | MATH |
[
{
"content": "How many solutions does the equation 2(-1|(2|x + 3| - 1) - 3| + 1)^2 + 3(-1|(2|x + 3| - 1) - 3| + 1) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8 | MATH |
[
{
"content": "How many zeros does the function f(x) = -2(3|(4x^2 + 3x - 2) - 3| + 2)^2 + 4(3|(4x^2 + 3x - 2) - 3| + 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) = -5(-1cos(3π(5x - 1) + 3) + 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 300 | MATH |
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