id stringlengths 34 34 | setting_key stringclasses 1
value | setting_name stringclasses 0
values | messages listlengths 1 1 | ground_truth stringclasses 166
values | dataset stringclasses 1
value |
|---|---|---|---|---|---|
trans_func_intersection_train_0100 | trans_func_intersection | null | [
{
"role": "user",
"content": "Determine the number of intersection points between the functions f(x) = -3sin(3π(1(1|x + 2| + 1) + 4) - 1) - 1 and g(x) = -3sin(3π(4x)) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 120 | math |
trans_func_intersection_train_0101 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many points of intersection exist between the functions f(x) = -1(-1|((-1(-2x + 1) + 3)/(3(-2x + 1) + 2)) + 1| + 1)^2 + 1(-1|((-1(-2x + 1) + 3)/(3(-2x + 1) + 2)) + 1| + 1) and g(x) = -2sin(3π(-3(3x^2 + 2x + 2) + 5) + 2) in the range -10 ≤ x ≤ 10?\n\nPresent the answer in La... | 1455 | math |
trans_func_intersection_train_0102 | trans_func_intersection | null | [
{
"role": "user",
"content": "Find the number of times the graphs of f(x) = (-3(5x^2 + 2x - 4) + 2)/(2(5x^2 + 2x - 4) - 3) and g(x) = 1|x + 1| - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
trans_func_intersection_train_0103 | trans_func_intersection | null | [
{
"role": "user",
"content": "Determine the number of intersection points between the functions f(x) = -2(-1(-2|((3x + 3)/(-2x + 3)) - 3|) + 3)^2 - 2(-1(-2|((3x + 3)/(-2x + 3)) - 3|) + 3) + 4 and g(x) = -2e^(2(5(1x^2 + 1x - 5) - 4)) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your... | 2 | math |
trans_func_intersection_train_0104 | trans_func_intersection | null | [
{
"role": "user",
"content": "Determine the number of intersection points between the functions f(x) = -2(-1((2(2|x - 2| - 1))/(-3(2|x - 2| - 1) + 1)) - 1)^2 - 2(-1((2(2|x - 2| - 1))/(-3(2|x - 2| - 1) + 1)) - 1) - 3 and g(x) = -3|(5(3x^2 - 3x + 2)) - 2| + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex... | 4 | math |
trans_func_intersection_train_0105 | trans_func_intersection | null | [
{
"role": "user",
"content": "Determine the number of intersection points between the functions f(x) = -1(3((2x + 3)/(2x - 1)) - 4)^2 + 3(3((2x + 3)/(2x - 1)) - 4) - 1 and g(x) = 1cos(3π(1x + 2) + 2) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 14 | math |
trans_func_intersection_train_0106 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many points of intersection exist between the functions f(x) = 2|((-2(-5(2x^2 + 3x + 3) - 2) - 1)/(2(-5(2x^2 + 3x + 3) - 2) + 3))| + 1 and g(x) = -2(3|((-1x + 2)/(-3x - 1)) - 1| - 1)^2 - 2(3|((-1x + 2)/(-3x - 1)) - 1| - 1) + 3 in the range -10 ≤ x ≤ 10?\n\nPresent the answe... | 4 | math |
trans_func_intersection_train_0107 | trans_func_intersection | null | [
{
"role": "user",
"content": "Find the number of times the graphs of f(x) = (2(-2x + 4) - 2)/(3(-2x + 4) - 2) and g(x) = (1x - 1)/(-1x + 2) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
trans_func_intersection_train_0108 | trans_func_intersection | null | [
{
"role": "user",
"content": "Find the number of times the graphs of f(x) = 3(5((1x + 2)/(2x + 3)))^2 - 5(5((1x + 2)/(2x + 3))) - 2 and g(x) = 4(1sin(3πx) + 3)^2 + 3(1sin(3πx) + 3) - 4 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 4 | math |
trans_func_intersection_train_0109 | trans_func_intersection | null | [
{
"role": "user",
"content": "Find the number of times the graphs of f(x) = (3(1|(3x^2 - 2x + 2) + 2| - 2))/(-2(1|(3x^2 - 2x + 2) + 2| - 2) - 2) and g(x) = -3cos(1π(-4x^2 - 1) + 2) + 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
trans_func_intersection_train_0110 | trans_func_intersection | null | [
{
"role": "user",
"content": "Find the number of times the graphs of f(x) = (-1(2(2|(1x^2 + 4)|) + 3) - 1)/(2(2(2|(1x^2 + 4)|) + 3) - 3) and g(x) = 1cos(2π(-3(1|x + 1| + 3) + 3) - 2) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 120 | math |
trans_func_intersection_train_0111 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many solutions does the equation -1(-2|(3((-1x - 2)/(-3x - 3))^2 - 4((-1x - 2)/(-3x - 3)) - 2) - 2| - 2) + 5 = -4(2sin(1π(-3|x + 3|) - 3) - 3) - 1 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 58 | math |
trans_func_intersection_train_0112 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many points of intersection exist between the functions f(x) = 2|(-3cos(2πx - 2) + 3) - 2| - 1 and g(x) = (-2x + 3)/(3x - 2) in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 73 | math |
trans_func_intersection_train_0113 | trans_func_intersection | null | [
{
"role": "user",
"content": "Determine the number of intersection points between the functions f(x) = -4(-2|(-3x^2 - 4x + 3) + 2| + 2) - 1 and g(x) = -1((-2x)/(1x - 3)) - 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 5 | math |
trans_func_intersection_train_0114 | trans_func_intersection | null | [
{
"role": "user",
"content": "Determine the number of intersection points between the functions f(x) = 1(3sin(1πx - 2) + 1) - 2 and g(x) = -2|x - 1| - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 4 | math |
trans_func_intersection_train_0115 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many solutions does the equation -1sin(3π((1x - 1)/(1x + 3)) - 2) = (1x + 3)/(-2x - 1) have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 127 | math |
trans_func_intersection_train_0116 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many solutions does the equation (-1(-2e^(2(2x + 4)) - 2) - 1)/(1(-2e^(2(2x + 4)) - 2) + 1) = (-3(2x^2 + 5x - 3) - 3)/(-2(2x^2 + 5x - 3) + 3) have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
trans_func_intersection_train_0117 | trans_func_intersection | null | [
{
"role": "user",
"content": "Find the number of times the graphs of f(x) = 5(5(2cos(1π(-3|x - 1| - 1) + 1) + 2)^2 + 5(2cos(1π(-3|x - 1| - 1) + 1) + 2) - 1) - 2 and g(x) = (-2(-2|(-4x + 5)| + 1) - 2)/(-2(-2|(-4x + 5)| + 1)) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{... | 63 | math |
trans_func_intersection_train_0118 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many solutions does the equation (1(2cos(2πx - 1) + 2) + 2)/(-1(2cos(2πx - 1) + 2) - 3) = -1x^2 + 2x + 2 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
trans_func_intersection_train_0119 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many solutions does the equation (1(-1x + 3) + 2)/(-3(-1x + 3) + 2) = -5x - 2 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
trans_func_intersection_train_0120 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many solutions does the equation (3(-5(-3x + 4)^2 - 2(-3x + 4) - 3))/(3(-5(-3x + 4)^2 - 2(-3x + 4) - 3) + 3) = -2(3sin(3πx + 3) + 2) + 3 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 60 | math |
trans_func_intersection_train_0121 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many points of intersection exist between the functions f(x) = (-2(4(1|(2sin(2πx - 2) + 1) + 2| - 1) + 3))/(-3(4(1|(2sin(2πx - 2) + 1) + 2| - 1) + 3) + 4) and g(x) = 3e^(-1(1(-2|x + 2| + 1))) - 2 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your... | 2 | math |
trans_func_intersection_train_0122 | trans_func_intersection | null | [
{
"role": "user",
"content": "Find the number of times the graphs of f(x) = 2|((-3(4x - 2))/(3(4x - 2) + 3)) + 3| + 2 and g(x) = 1e^(1(-2|x + 1| + 2)) + 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 4 | math |
trans_func_intersection_train_0123 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many points of intersection exist between the functions f(x) = -1|((-2x - 3)/(1x - 2)) - 3| + 3 and g(x) = 3x^2 + 2x - 3 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
trans_func_intersection_train_0124 | trans_func_intersection | null | [
{
"role": "user",
"content": "Determine the number of intersection points between the functions f(x) = (1(3|(-4(-1x^2 - 5x - 4) + 5) - 3|) + 3)/(1(3|(-4(-1x^2 - 5x - 4) + 5) - 3|) - 2) and g(x) = -1|(3e^(1(1x^2 - 2x - 3)) + 3)| + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 2 | math |
trans_func_intersection_train_0125 | trans_func_intersection | null | [
{
"role": "user",
"content": "Find the number of times the graphs of f(x) = (2(1|(1(-3x - 4)^2 + 3(-3x - 4) - 1) + 3| - 2) - 1)/(-2(1|(1(-3x - 4)^2 + 3(-3x - 4) - 1) + 3| - 2)) and g(x) = (1(2cos(1π(1x + 3) - 3) + 1) + 1)/(-2(2cos(1π(1x + 3) - 3) + 1) + 1) intersect in the interval [-10, 10].\n\nPresent the... | 22 | math |
trans_func_intersection_train_0126 | trans_func_intersection | null | [
{
"role": "user",
"content": "Determine the number of intersection points between the functions f(x) = 5(2sin(1πx + 2) - 2) + 3 and g(x) = (-1x - 3)/(3x) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 19 | math |
trans_func_intersection_train_0127 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many points of intersection exist between the functions f(x) = 1((2(-1|(-4x^2 - 2x - 1) + 2| - 2) + 3)/(2(-1|(-4x^2 - 2x - 1) + 2| - 2) + 3)) - 1 and g(x) = (-2(-5(3|x - 2| - 1) - 2) + 1)/(-3(-5(3|x - 2| - 1) - 2) - 1) in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaT... | 2 | math |
trans_func_intersection_train_0128 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many points of intersection exist between the functions f(x) = (-2(-1x - 4))/(-1(-1x - 4) - 1) and g(x) = 1x^2 - 5x - 4 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
trans_func_intersection_train_0129 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many solutions does the equation 5(-1((-1(-2|x - 1| - 1) - 3)/(-3(-2|x - 1| - 1) - 3))^2 - 3((-1(-2|x - 1| - 1) - 3)/(-3(-2|x - 1| - 1) - 3)) - 3) + 4 = -1|(3((-2x + 3)/(-2x)) - 1) - 2| - 2 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed... | 4 | math |
trans_func_intersection_train_0130 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many points of intersection exist between the functions f(x) = 3|(3e^(-1(1(1x + 5)^2 - 1(1x + 5))) + 2) - 2| - 1 and g(x) = (2(5(-1x^2 - 2x - 1) + 5) - 1)/(1(5(-1x^2 - 2x - 1) + 5)) in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
... | 4 | math |
trans_func_intersection_train_0131 | trans_func_intersection | null | [
{
"role": "user",
"content": "Find the number of times the graphs of f(x) = (3(2(-3(2|x - 2|)^2 + 4(2|x - 2|) - 1) + 5) - 1)/(-2(2(-3(2|x - 2|)^2 + 4(2|x - 2|) - 1) + 5) + 3) and g(x) = (-3(2e^(1(-2|x + 3| + 3)) + 1) + 1)/(-2(2e^(1(-2|x + 3| + 3)) + 1) - 3) intersect in the interval [-10, 10].\n\nPresent th... | 2 | math |
trans_func_intersection_train_0132 | trans_func_intersection | null | [
{
"role": "user",
"content": "Determine the number of intersection points between the functions f(x) = 2|(-2(-2((3x - 3)/(1x + 1)) + 2)^2 + 2(-2((3x - 3)/(1x + 1)) + 2) + 1) - 3| + 2 and g(x) = -1(1e^(-1(-1|x - 1| + 2)) - 2)^2 - 3(1e^(-1(-1|x - 1| + 2)) - 2) + 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in ... | 2 | math |
trans_func_intersection_train_0133 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many points of intersection exist between the functions f(x) = 2(3|(-3((-3x + 1)/(3x + 2)) + 4) - 2| - 1)^2 - 3(3|(-3((-3x + 1)/(3x + 2)) + 4) - 2| - 1) - 2 and g(x) = (-3(-1(-2sin(2πx + 1) + 3) + 2) + 3)/(2(-1(-2sin(2πx + 1) + 3) + 2)) in the range -10 ≤ x ≤ 10?\n\nPresent... | 4 | math |
trans_func_intersection_train_0134 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many solutions does the equation 1(1(-2|((-1x - 1)/(-1x + 2)) - 2| + 3) - 5)^2 + 5(1(-2|((-1x - 1)/(-1x + 2)) - 2| + 3) - 5) - 4 = 1|((1(2x - 3) + 2)/(1(2x - 3) - 2)) - 2| + 1 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 4 | math |
trans_func_intersection_train_0135 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many solutions does the equation 1|(-4(-2e^(-1x) + 3)^2 + 4)| = 1|(-1x^2 - 5x - 4) + 1| + 2 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 5 | math |
trans_func_intersection_train_0136 | trans_func_intersection | null | [
{
"role": "user",
"content": "Find the number of times the graphs of f(x) = -3((3(4x + 5) + 3)/(3(4x + 5) - 2))^2 + 2((3(4x + 5) + 3)/(3(4x + 5) - 2)) and g(x) = 1cos(1π(5x^2 + 2x - 2) + 1) - 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 6 | math |
trans_func_intersection_train_0137 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many points of intersection exist between the functions f(x) = (1(2(-3cos(3π(-1|x + 2| + 1) + 1) - 2) + 3) - 2)/(-3(2(-3cos(3π(-1|x + 2| + 1) + 1) - 2) + 3) - 3) and g(x) = 1cos(1π(-5(4x^2 + 2x - 5) - 1) - 1) + 3 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex for... | 59 | math |
trans_func_intersection_train_0138 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many solutions does the equation -1|(-1sin(2π(1x + 2) - 2)) + 3| + 1 = 1(2e^(2x)) - 1 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 4 | math |
trans_func_intersection_train_0139 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many solutions does the equation -4(5(-2cos(1πx + 1) + 1) + 2)^2 - 2(5(-2cos(1πx + 1) + 1) + 2) + 2 = -3(-3|x - 1| + 3) - 3 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 8 | math |
trans_func_intersection_train_0140 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many points of intersection exist between the functions f(x) = 2(2|(-2sin(1π((2x - 1)/(3x))) - 2) - 3| - 3) + 4 and g(x) = 3|(-1cos(1π(4x - 1)) + 3)| + 2 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 18 | math |
trans_func_intersection_train_0141 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many solutions does the equation -1|((-1(3e^(2x) + 3))/(-2(3e^(2x) + 3) + 3)) - 3| + 2 = 1|(3sin(2πx) - 1) + 1| - 3 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 60 | math |
trans_func_intersection_train_0142 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many points of intersection exist between the functions f(x) = (1(-2cos(3π(-4(5x^2 - 4x)) - 3) + 2) + 2)/(-1(-2cos(3π(-4(5x^2 - 4x)) - 3) + 2) + 2) and g(x) = 1(2sin(2π(-1|x - 2| + 1) - 3) + 1) - 1 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Yo... | 352 | math |
trans_func_intersection_train_0143 | trans_func_intersection | null | [
{
"role": "user",
"content": "Find the number of times the graphs of f(x) = -5(4((3x + 2)/(-1x - 1))^2 - 1((3x + 2)/(-1x - 1)) - 1) and g(x) = -3(1sin(1πx - 1) + 2) + 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
trans_func_intersection_train_0144 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many solutions does the equation -1(-1((2(3|x + 3| - 2) + 3)/(1(3|x + 3| - 2) + 3))^2 + 4((2(3|x + 3| - 2) + 3)/(1(3|x + 3| - 2) + 3)) - 2) - 3 = -2|(3(-2e^(2x) + 1) + 4) - 3| - 2 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 2 | math |
trans_func_intersection_train_0145 | trans_func_intersection | null | [
{
"role": "user",
"content": "Determine the number of intersection points between the functions f(x) = -1|((-2(4(-5x + 3)^2 - 1(-5x + 3) - 4) + 3)/(3(4(-5x + 3)^2 - 1(-5x + 3) - 4) + 2)) + 1| and g(x) = 1|((-1(4x^2 - 2) + 1)/(2(4x^2 - 2) - 1)) + 2| - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex form... | 2 | math |
trans_func_intersection_train_0146 | trans_func_intersection | null | [
{
"role": "user",
"content": "Find the number of times the graphs of f(x) = 1(-1(1|((-3x - 3)/(2x - 3)) - 2| - 1) + 3)^2 - 4(-1(1|((-3x - 3)/(2x - 3)) - 2| - 1) + 3) - 4 and g(x) = -3cos(2π(-2((-2x - 3)/(-2x - 1)) - 1) - 3) - 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\bo... | 4 | math |
trans_func_intersection_train_0147 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many points of intersection exist between the functions f(x) = -4(-2cos(1πx - 3) + 2)^2 - 3(-2cos(1πx - 3) + 2) + 5 and g(x) = 1x^2 - 3x - 1 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 6 | math |
trans_func_intersection_train_0148 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many points of intersection exist between the functions f(x) = -2sin(1π(1((1(2x^2 - 4) + 2)/(-2(2x^2 - 4) + 3)) - 4)) + 2 and g(x) = (-3(1(1x^2 + 2x - 4) + 4) + 1)/(-2(1(1x^2 + 2x - 4) + 4) + 3) in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your ... | 40 | math |
trans_func_intersection_train_0149 | trans_func_intersection | null | [
{
"role": "user",
"content": "Find the number of times the graphs of f(x) = -5(3sin(1πx) - 1)^2 - 2(3sin(1πx) - 1) + 5 and g(x) = 1|x + 3| - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 26 | math |
trans_func_intersection_train_0150 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many points of intersection exist between the functions f(x) = -3|((-2(-4x^2 - 5x - 4) - 2)/(-1(-4x^2 - 5x - 4)))| - 3 and g(x) = -1(-3sin(2πx + 1) + 2)^2 - 3(-3sin(2πx + 1) + 2) in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 40 | math |
trans_func_intersection_train_0151 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many points of intersection exist between the functions f(x) = -1e^(2((-1(5x^2 - 5x - 4) - 2)/(-3(5x^2 - 5x - 4) - 2))) + 2 and g(x) = (2(1sin(3πx) + 2) - 3)/(2(1sin(3πx) + 2) + 3) in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 50 | math |
trans_func_intersection_train_0152 | trans_func_intersection | null | [
{
"role": "user",
"content": "Determine the number of intersection points between the functions f(x) = (2(2(-2e^(1(-2|x| + 3)) + 1)) - 1)/(2(2(-2e^(1(-2|x| + 3)) + 1)) + 3) and g(x) = -4((3(3x^2 - 1x - 4) + 2)/(-1(3x^2 - 1x - 4) - 2)) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 4 | math |
trans_func_intersection_train_0153 | trans_func_intersection | null | [
{
"role": "user",
"content": "Find the number of times the graphs of f(x) = 3(-2|(-4((1x - 1)/(2x)) - 4) + 3| + 2)^2 + 1(-2|(-4((1x - 1)/(2x)) - 4) + 3| + 2) - 4 and g(x) = (1(-1sin(3π(2|x + 1| + 3) + 2) - 2))/(-2(-1sin(3π(2|x + 1| + 3) + 2) - 2) + 3) intersect in the interval [-10, 10].\n\nPresent the answ... | 4 | math |
trans_func_intersection_train_0154 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many points of intersection exist between the functions f(x) = 2(-2(-1|((-1x + 1)/(-2x + 1)) + 1| - 1) + 3)^2 - 1 and g(x) = 2(5((3x + 3)/(-2x + 3))^2 - 1((3x + 3)/(-2x + 3)) - 1) - 3 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
... | 2 | math |
trans_func_intersection_train_0155 | trans_func_intersection | null | [
{
"role": "user",
"content": "Determine the number of intersection points between the functions f(x) = 1|(1(1sin(3π(2x + 4) - 3))^2 - 3(1sin(3π(2x + 4) - 3)) - 1) + 2| - 2 and g(x) = (-1(1sin(2π(-1x + 4) + 2) - 2) - 2)/(3(1sin(2π(-1x + 4) + 2) - 2) + 3) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex for... | 80 | math |
trans_func_intersection_train_0156 | trans_func_intersection | null | [
{
"role": "user",
"content": "Determine the number of intersection points between the functions f(x) = 4((-1(-1|(2e^(-1x)) + 1| + 1) + 3)/(2(-1|(2e^(-1x)) + 1| + 1) + 1)) + 4 and g(x) = 1cos(3π(5(-3|x - 2| + 2) + 2)) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 41 | math |
trans_func_intersection_train_0157 | trans_func_intersection | null | [
{
"role": "user",
"content": "Find the number of times the graphs of f(x) = 3sin(1π(3(-2x - 2)^2 + 5(-2x - 2) + 2) + 3) + 3 and g(x) = 3(2sin(3πx - 3) + 3) - 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 453 | math |
trans_func_intersection_train_0158 | trans_func_intersection | null | [
{
"role": "user",
"content": "Determine the number of intersection points between the functions f(x) = (-2(-1|(5x)| + 1) + 3)/(2(-1|(5x)| + 1) + 2) and g(x) = -4(3|x|) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 4 | math |
trans_func_intersection_train_0159 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many points of intersection exist between the functions f(x) = 1cos(3π((-2(3(-5x + 2)^2 - 3) - 2)/(-2(3(-5x + 2)^2 - 3))) + 3) - 1 and g(x) = 3cos(3π(-5((3x + 3)/(3x)) + 2) + 2) - 3 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
... | 79 | math |
trans_func_intersection_train_0160 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many solutions does the equation (1(1x + 3) - 1)/(2(1x + 3) - 1) = 3x + 4 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
trans_func_intersection_train_0161 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many solutions does the equation -5((-2(1|(-2x + 5) - 2| - 3) + 3)/(-2(1|(-2x + 5) - 2| - 3) - 1))^2 + 5((-2(1|(-2x + 5) - 2| - 3) + 3)/(-2(1|(-2x + 5) - 2| - 3) - 1)) + 3 = (3(3(4x - 2)^2 - 2(4x - 2) - 1) + 3)/(-1(3(4x - 2)^2 - 2(4x - 2) - 1) - 2) have for x in the interva... | 2 | math |
trans_func_intersection_train_0162 | trans_func_intersection | null | [
{
"role": "user",
"content": "Determine the number of intersection points between the functions f(x) = -3|(-3cos(3πx + 2) - 2) + 1| + 1 and g(x) = 4x + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 13 | math |
trans_func_intersection_train_0163 | trans_func_intersection | null | [
{
"role": "user",
"content": "Find the number of times the graphs of f(x) = 2|(1(-3x^2 - 1x + 4) - 4) + 1| - 3 and g(x) = 3sin(2π(2|x + 2| - 1) + 3) + 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 8 | math |
trans_func_intersection_train_0164 | trans_func_intersection | null | [
{
"role": "user",
"content": "Determine the number of intersection points between the functions f(x) = -3(-4(3|((-2x - 3)/(3x + 3)) - 1| - 2)^2 - 1(3|((-2x - 3)/(3x + 3)) - 1| - 2) + 1) - 4 and g(x) = 2sin(1π(-1(1|x - 3| + 3)^2 - 5(1|x - 3| + 3) - 2)) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex f... | 4 | math |
trans_func_intersection_train_0165 | trans_func_intersection | null | [
{
"role": "user",
"content": "Determine the number of intersection points between the functions f(x) = 2|(3cos(3π(1((1x - 1)/(-3x + 1))^2 + 1((1x - 1)/(-3x + 1)) - 2) + 3) + 2) - 2| + 3 and g(x) = -3(-2cos(3π(2|x| - 1) + 2) + 1) + 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your ans... | 124 | math |
trans_func_intersection_train_0166 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many solutions does the equation (-2(3|(4(-1x + 3)^2 + 2(-1x + 3) - 4) - 2| - 3) + 1)/(-1(3|(4(-1x + 3)^2 + 2(-1x + 3) - 4) - 2| - 3)) = 1sin(1π(-2|(-4x^2 + 2x + 4)| - 1) - 2) - 3 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answ... | 4 | math |
trans_func_intersection_train_0167 | trans_func_intersection | null | [
{
"role": "user",
"content": "Determine the number of intersection points between the functions f(x) = 1((-2(5x) + 3)/(2(5x) + 2))^2 - 1((-2(5x) + 3)/(2(5x) + 2)) - 5 and g(x) = (-2(-3x^2 + 4x - 4))/(-1(-3x^2 + 4x - 4) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}... | 2 | math |
trans_func_intersection_train_0168 | trans_func_intersection | null | [
{
"role": "user",
"content": "Find the number of times the graphs of f(x) = 3cos(3π(-2x + 1) + 2) and g(x) = 2x - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 19 | math |
trans_func_intersection_train_0169 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many points of intersection exist between the functions f(x) = -4(-2x^2 - 5x - 1) + 2 and g(x) = (2x + 3)/(1x) in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
trans_func_intersection_train_0170 | trans_func_intersection | null | [
{
"role": "user",
"content": "Determine the number of intersection points between the functions f(x) = (2(-3|x + 2| + 1) + 2)/(1(-3|x + 2| + 1) - 3) and g(x) = -2|x - 2| + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
trans_func_intersection_train_0171 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many solutions does the equation -4(2|((-1x)/(2x - 3)) + 1| - 3) + 1 = 1(5x + 3)^2 + 5(5x + 3) + 1 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
trans_func_intersection_train_0172 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many points of intersection exist between the functions f(x) = (2(-4x^2 - 2x + 4) - 1)/(3(-4x^2 - 2x + 4) + 3) and g(x) = 1|x - 1| + 1 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
trans_func_intersection_train_0173 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many solutions does the equation 2|(-5(-3sin(3πx))^2 - 3(-3sin(3πx)) + 3) + 3| + 3 = (1(-2x^2 + 4x - 1) - 2)/(1(-2x^2 + 4x - 1) + 2) have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 8 | math |
trans_func_intersection_train_0174 | trans_func_intersection | null | [
{
"role": "user",
"content": "Determine the number of intersection points between the functions f(x) = 1|(-4(2sin(2π(5x - 4) - 3))^2 + 3(2sin(2π(5x - 4) - 3)) + 3) - 3| - 2 and g(x) = (2(-1sin(3π(-2|x - 3| - 3) - 2) + 2) + 3)/(3(-1sin(3π(-2|x - 3| - 3) - 2) + 2) + 2) where -10 ≤ x ≤ 10.\n\nPresent the answe... | 400 | math |
trans_func_intersection_train_0175 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many solutions does the equation 2|((-2x)/(-3x - 1)) + 2| - 2 = 1x^2 + 2x + 4 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
trans_func_intersection_train_0176 | trans_func_intersection | null | [
{
"role": "user",
"content": "Find the number of times the graphs of f(x) = (1(-1|(1x - 1) + 1| + 2) - 1)/(2(-1|(1x - 1) + 1| + 2)) and g(x) = (2(-1cos(3πx + 1) + 2) + 3)/(-2(-1cos(3πx + 1) + 2) + 1) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
trans_func_intersection_train_0177 | trans_func_intersection | null | [
{
"role": "user",
"content": "Determine the number of intersection points between the functions f(x) = -1|((2(-1(-4x^2 - 5x) + 3) - 2)/(-1(-1(-4x^2 - 5x) + 3) + 2)) + 2| - 2 and g(x) = -1(-2cos(1π(-3|x - 2| - 3) + 1) - 3)^2 + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"... | 60 | math |
trans_func_intersection_train_0178 | trans_func_intersection | null | [
{
"role": "user",
"content": "Find the number of times the graphs of f(x) = (-1(1(-2|x| + 1)^2 - 5(-2|x| + 1) - 2) + 3)/(2(1(-2|x| + 1)^2 - 5(-2|x| + 1) - 2) - 1) and g(x) = 2(-4x - 4)^2 - 5(-4x - 4) - 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
trans_func_intersection_train_0179 | trans_func_intersection | null | [
{
"role": "user",
"content": "Find the number of times the graphs of f(x) = 5((3(-2|(2x - 2) + 2| + 3))/(-1(-2|(2x - 2) + 2| + 3) - 1))^2 + 3((3(-2|(2x - 2) + 2| + 3))/(-1(-2|(2x - 2) + 2| + 3) - 1)) + 4 and g(x) = -5(-3|(-3x^2 - 3x - 5)| + 1) - 1 intersect in the interval [-10, 10].\n\nPresent the answer i... | 4 | math |
trans_func_intersection_train_0180 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many solutions does the equation -3(-2cos(1πx + 1) - 2) + 2 = 3x + 5 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
trans_func_intersection_train_0181 | trans_func_intersection | null | [
{
"role": "user",
"content": "Find the number of times the graphs of f(x) = -1|((1(3(-2x - 4)^2 - 1) - 2)/(-2(3(-2x - 4)^2 - 1) - 2)) - 1| - 2 and g(x) = -1|(-2((2x + 3)/(-2x)) + 5)| - 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 4 | math |
trans_func_intersection_train_0182 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many solutions does the equation (-2(-1(3|(-1x - 1) - 2| + 2)^2 + 4(3|(-1x - 1) - 2| + 2) + 4) - 1)/(2(-1(3|(-1x - 1) - 2| + 2)^2 + 4(3|(-1x - 1) - 2| + 2) + 4) + 3) = -3((1(-1|x|) - 2)/(-2(-1|x|) + 1))^2 + 3 have for x in the interval [-10, 10]?\n\nPresent the answer in La... | 4 | math |
trans_func_intersection_train_0183 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many points of intersection exist between the functions f(x) = 1|(-2sin(1πx + 2) - 3) + 3| + 2 and g(x) = 1x^2 - 5x + 3 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
trans_func_intersection_train_0184 | trans_func_intersection | null | [
{
"role": "user",
"content": "Find the number of times the graphs of f(x) = (-1(-1|(5(-3cos(2πx + 3) - 3) + 5) + 2| + 2) - 3)/(-1(-1|(5(-3cos(2πx + 3) - 3) + 5) + 2| + 2) + 2) and g(x) = -2|(2cos(3π(-2x^2 - 2x + 5) + 2)) + 1| - 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\... | 78 | math |
trans_func_intersection_train_0185 | trans_func_intersection | null | [
{
"role": "user",
"content": "Find the number of times the graphs of f(x) = 2|(-1(-1e^(-2((-3x)/(-1x))) + 3) - 3) + 1| - 1 and g(x) = 1e^(-2(-1((-3x - 2)/(-3x - 1))^2 + 5((-3x - 2)/(-3x - 1)) - 4)) - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
trans_func_intersection_train_0186 | trans_func_intersection | null | [
{
"role": "user",
"content": "Determine the number of intersection points between the functions f(x) = -4(-1|(1e^(-1x) - 2) - 2| + 1) and g(x) = -1sin(3π((2x + 3)/(-3x + 4)) - 1) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
trans_func_intersection_train_0187 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many solutions does the equation (3(3x + 4))/(2(3x + 4) + 3) = 1|x - 1| have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
trans_func_intersection_train_0188 | trans_func_intersection | null | [
{
"role": "user",
"content": "Determine the number of intersection points between the functions f(x) = -1sin(3π(-1x - 4) - 1) and g(x) = -2x - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
trans_func_intersection_train_0189 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many points of intersection exist between the functions f(x) = -2(1cos(3π(-2|((-2x - 1)/(2x + 2)) - 2| - 3) - 1) + 2)^2 + 5 and g(x) = (-3(-3e^(-2(3x)) + 1) + 2)/(3(-3e^(-2(3x)) + 1) + 2) in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}... | 63 | math |
trans_func_intersection_train_0190 | trans_func_intersection | null | [
{
"role": "user",
"content": "Find the number of times the graphs of f(x) = -3sin(3π(2((-2x - 2)/(1x - 3))^2 - 4((-2x - 2)/(1x - 3)) - 5) + 3) - 2 and g(x) = (-1(1e^(2x) + 1) + 1)/(2(1e^(2x) + 1) + 3) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 474 | math |
trans_func_intersection_train_0191 | trans_func_intersection | null | [
{
"role": "user",
"content": "Find the number of times the graphs of f(x) = -3(-1|x + 3| + 1)^2 - 3(-1|x + 3| + 1) + 5 and g(x) = -5x intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
trans_func_intersection_train_0192 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many points of intersection exist between the functions f(x) = (1(2(-4(3sin(2πx - 3) + 2)^2 - 2(3sin(2πx - 3) + 2) + 5) - 1) + 2)/(2(2(-4(3sin(2πx - 3) + 2)^2 - 2(3sin(2πx - 3) + 2) + 5) - 1) - 1) and g(x) = 5(-1(-1|x - 1| + 1)^2 + 3(-1|x - 1| + 1) + 3) + 5 in the range -10... | 4 | math |
trans_func_intersection_train_0193 | trans_func_intersection | null | [
{
"role": "user",
"content": "Determine the number of intersection points between the functions f(x) = (2(1|(-1(-1x^2 + 4x + 2) + 2) + 1| - 1))/(-3(1|(-1(-1x^2 + 4x + 2) + 2) + 1| - 1) - 3) and g(x) = 3(-1cos(1π((-3x + 1)/(2x - 1)) - 3) + 3)^2 - 2(-1cos(1π((-3x + 1)/(2x - 1)) - 3) + 3) where -10 ≤ x ≤ 10.\n... | 4 | math |
trans_func_intersection_train_0194 | trans_func_intersection | null | [
{
"role": "user",
"content": "Find the number of times the graphs of f(x) = -5((-1(2(2sin(3πx - 1) - 1) - 3) - 3)/(1(2(2sin(3πx - 1) - 1) - 3) - 3))^2 + 3((-1(2(2sin(3πx - 1) - 1) - 3) - 3)/(1(2(2sin(3πx - 1) - 1) - 3) - 3)) and g(x) = 2(-5(1|x - 1| - 1)^2 - 5(1|x - 1| - 1) - 1) - 1 intersect in the interva... | 6 | math |
trans_func_intersection_train_0195 | trans_func_intersection | null | [
{
"role": "user",
"content": "Find the number of times the graphs of f(x) = -4(-1sin(1πx) + 1)^2 - 3 and g(x) = -2|x - 3| intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 16 | math |
trans_func_intersection_train_0196 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many solutions does the equation 4(-1sin(1πx + 3) + 2)^2 - 5(-1sin(1πx + 3) + 2) + 1 = 2|x + 3| - 2 have for x in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 18 | math |
trans_func_intersection_train_0197 | trans_func_intersection | null | [
{
"role": "user",
"content": "How many points of intersection exist between the functions f(x) = 4(-2|((-1x + 1)/(-2x - 2)) + 2| + 2) - 3 and g(x) = 2cos(1π(-2x^2 + 3x)) + 2 in the range -10 ≤ x ≤ 10?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
trans_func_intersection_train_0198 | trans_func_intersection | null | [
{
"role": "user",
"content": "Find the number of times the graphs of f(x) = (-2(-2(5(1|x + 3| - 3)^2 - 5) + 5) - 2)/(2(-2(5(1|x + 3| - 3)^2 - 5) + 5)) and g(x) = 1(-2e^(-1(-1x - 1)) - 3)^2 + 4(-2e^(-1(-1x - 1)) - 3) - 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your... | 4 | math |
trans_func_intersection_train_0199 | trans_func_intersection | null | [
{
"role": "user",
"content": "Find the number of times the graphs of f(x) = -1((1(3sin(2π(2|x - 2| - 2) - 3) + 1) - 3)/(2(3sin(2π(2|x - 2| - 2) - 3) + 1) - 1)) - 2 and g(x) = 1(-1|(-1e^(1x) + 3) + 1| + 2) - 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
... | 52 | math |
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