question stringlengths 109 170 | answer stringlengths 1 3 | type stringclasses 1 value | difficulty int64 9 57 |
|---|---|---|---|
Determine the number of intersection points between the functions f(x) = -3sin(3π(-2x - 4) + 1) and g(x) = -5x - 3 where -10 ≤ x ≤ 10. | 9 | intersection | 11 |
How many solutions does the equation 3sin(2π(-2x^2 + 5x - 1) + 1) = -5x^2 - 5x - 1 have for x in the interval [-10, 10]? | 22 | intersection | 18 |
Determine the number of intersection points between the functions f(x) = -3cos(2π(-5x + 4) + 2) and g(x) = (-3x - 3)/(2x - 3) where -10 ≤ x ≤ 10. | 167 | intersection | 55 |
How many solutions does the equation (-2(-3sin(1πx - 3) - 1) - 1)/(2(-3sin(1πx - 3) - 1) + 2) = -1x - 2 have for x in the interval [-10, 10]? | 21 | intersection | 18 |
How many solutions does the equation (1(2cos(1πx + 3) - 2) - 2)/(-2(2cos(1πx + 3) - 2) - 1) = -2x^2 + 1x - 1 have for x in the interval [-10, 10]? | 18 | intersection | 18 |
Find the number of times the graphs of f(x) = 1|(1x^2 - 4x - 1) - 2| - 2 and g(x) = 3|x - 2| - 2 intersect in the interval [-10, 10]. | 4 | intersection | 10 |
Determine the number of intersection points between the functions f(x) = 2cos(3π(5x + 2)) + 1 and g(x) = 1x^2 - 5x + 4 where -10 ≤ x ≤ 10. | 34 | intersection | 21 |
Find the number of times the graphs of f(x) = -1|(3sin(3πx - 3) - 1) + 1| + 1 and g(x) = 3x - 2 intersect in the interval [-10, 10]. | 7 | intersection | 12 |
How many solutions does the equation -3sin(1π(4x - 5) - 1) + 2 = 1x - 4 have for x in the interval [-10, 10]? | 23 | intersection | 16 |
How many solutions does the equation 3sin(3π(-1x + 3) + 1) - 1 = -2|x + 3| + 2 have for x in the interval [-10, 10]? | 18 | intersection | 16 |
How many points of intersection exist between the functions f(x) = (3(1cos(2πx - 3)) - 2)/(-3(1cos(2πx - 3)) + 1) and g(x) = (3x - 3)/(3x + 2) in the range -10 ≤ x ≤ 10? | 41 | intersection | 28 |
How many solutions does the equation 2cos(1π(3|x + 3| + 2) + 3) - 1 = (2x + 3)/(-2x + 3) have for x in the interval [-10, 10]? | 51 | intersection | 30 |
Determine the number of intersection points between the functions f(x) = 2cos(3π(2|x - 1| - 2) - 1) + 3 and g(x) = 1x + 1 where -10 ≤ x ≤ 10. | 23 | intersection | 18 |
How many solutions does the equation (1(1x^2 - 3x - 4) + 3)/(1(1x^2 - 3x - 4) - 3) = 2|x + 3| + 1 have for x in the interval [-10, 10]? | 4 | intersection | 11 |
Determine the number of intersection points between the functions f(x) = -2cos(3π((2x + 3)/(1x - 2))) and g(x) = 2x^2 + 5x where -10 ≤ x ≤ 10. | 4 | intersection | 12 |
Determine the number of intersection points between the functions f(x) = 1(1cos(2πx + 2))^2 + 5 and g(x) = -1x - 3 where -10 ≤ x ≤ 10. | 5 | intersection | 10 |
How many solutions does the equation 3cos(1π((3x - 1)/(-1x - 3)) + 1) + 2 = 4x^2 + 3x - 4 have for x in the interval [-10, 10]? | 4 | intersection | 12 |
How many points of intersection exist between the functions f(x) = -3sin(1π(-4x - 1) + 3) - 1 and g(x) = (-1x + 3)/(2x - 1) in the range -10 ≤ x ≤ 10? | 76 | intersection | 34 |
How many solutions does the equation (-3(2cos(3πx)) - 2)/(-1(2cos(3πx)) - 1) = -2x^2 - 4x + 4 have for x in the interval [-10, 10]? | 29 | intersection | 22 |
How many solutions does the equation 3cos(3π(-1x^2 + 3x - 5) - 2) + 3 = 3x^2 - 3x - 5 have for x in the interval [-10, 10]? | 10 | intersection | 13 |
Find the number of times the graphs of f(x) = 4(-1sin(3πx) - 2) - 3 and g(x) = -2|x - 3| + 2 intersect in the interval [-10, 10]. | 20 | intersection | 17 |
How many points of intersection exist between the functions f(x) = -2sin(3π(2|x - 2| + 1) + 3) + 1 and g(x) = -3|x - 3| + 2 in the range -10 ≤ x ≤ 10? | 12 | intersection | 16 |
Determine the number of intersection points between the functions f(x) = -3cos(2π(-5x^2 - 2x - 5)) - 2 and g(x) = 5x + 2 where -10 ≤ x ≤ 10. | 13 | intersection | 13 |
Find the number of times the graphs of f(x) = (2(2sin(1πx)) - 2)/(1(2sin(1πx))) and g(x) = -2|x + 3| - 3 intersect in the interval [-10, 10]. | 20 | intersection | 20 |
How many points of intersection exist between the functions f(x) = -3|(-2cos(3πx + 2) - 1) + 3| + 3 and g(x) = (1x + 2)/(-1x + 2) in the range -10 ≤ x ≤ 10? | 55 | intersection | 31 |
Determine the number of intersection points between the functions f(x) = -3(1cos(2πx) + 3)^2 + 5(1cos(2πx) + 3) + 3 and g(x) = -1x^2 + 1x - 2 where -10 ≤ x ≤ 10. | 20 | intersection | 17 |
How many solutions does the equation 3sin(3π((3x - 1)/(-3x)) + 1) = 1|x + 1| - 3 have for x in the interval [-10, 10]? | 32 | intersection | 24 |
Find the number of times the graphs of f(x) = 5(-2cos(2πx + 3)) - 1 and g(x) = 1|x - 3| - 3 intersect in the interval [-10, 10]. | 39 | intersection | 23 |
How many solutions does the equation -1cos(3π(1x^2 - 3x + 5) + 2) + 1 = 5x^2 - 4x - 3 have for x in the interval [-10, 10]? | 4 | intersection | 10 |
How many points of intersection exist between the functions f(x) = 2cos(1π(5x - 1) + 2) + 1 and g(x) = (1x + 1)/(-1x) in the range -10 ≤ x ≤ 10? | 49 | intersection | 27 |
Determine the number of intersection points between the functions f(x) = -1cos(3π(-3x - 2) - 1) - 1 and g(x) = (-1x)/(3x - 1) where -10 ≤ x ≤ 10. | 177 | intersection | 57 |
How many points of intersection exist between the functions f(x) = -3(2sin(2πx + 1) + 3)^2 + 1(2sin(2πx + 1) + 3) and g(x) = 3x + 1 in the range -10 ≤ x ≤ 10? | 18 | intersection | 15 |
How many points of intersection exist between the functions f(x) = -1((3x + 1)/(2x + 1))^2 - 5((3x + 1)/(2x + 1)) - 2 and g(x) = -2x^2 - 1x + 1 in the range -10 ≤ x ≤ 10? | 4 | intersection | 10 |
Determine the number of intersection points between the functions f(x) = (-3(2cos(2πx + 3) + 1) - 2)/(-2(2cos(2πx + 3) + 1) - 1) and g(x) = -1x^2 + 4x where -10 ≤ x ≤ 10. | 22 | intersection | 20 |
Determine the number of intersection points between the functions f(x) = 4(3sin(2πx - 3)) - 1 and g(x) = 1|x - 3| + 2 where -10 ≤ x ≤ 10. | 32 | intersection | 21 |
Find the number of times the graphs of f(x) = 3sin(3π((-2x - 2)/(3x)) - 3) + 1 and g(x) = -4x^2 - 4x + 5 intersect in the interval [-10, 10]. | 8 | intersection | 14 |
Find the number of times the graphs of f(x) = 2cos(3π(-1x + 4) + 2) + 3 and g(x) = -2x^2 - 3x + 4 intersect in the interval [-10, 10]. | 10 | intersection | 12 |
How many points of intersection exist between the functions f(x) = 1(-3cos(1πx - 2) - 3)^2 + 2(-3cos(1πx - 2) - 3) - 4 and g(x) = 3|x - 1| in the range -10 ≤ x ≤ 10? | 14 | intersection | 16 |
How many points of intersection exist between the functions f(x) = 1cos(3π(4x^2 + 4x - 2) - 3) and g(x) = -2x^2 + 4x in the range -10 ≤ x ≤ 10? | 35 | intersection | 22 |
Find the number of times the graphs of f(x) = 3(-2cos(2πx - 2)) - 2 and g(x) = -1|x + 3| - 2 intersect in the interval [-10, 10]. | 24 | intersection | 18 |
Find the number of times the graphs of f(x) = 4(3cos(3πx + 2) - 1) - 5 and g(x) = -4x - 1 intersect in the interval [-10, 10]. | 19 | intersection | 15 |
How many points of intersection exist between the functions f(x) = 1(-2cos(2πx - 1) - 3) + 1 and g(x) = -2x^2 - 2x + 1 in the range -10 ≤ x ≤ 10? | 4 | intersection | 9 |
How many solutions does the equation -1sin(2π(-3|x + 1|) + 1) - 1 = (-3x + 3)/(-2x - 2) have for x in the interval [-10, 10]? | 7 | intersection | 15 |
Find the number of times the graphs of f(x) = 3cos(3π(1x + 4)) - 1 and g(x) = -3|x + 2| + 3 intersect in the interval [-10, 10]. | 14 | intersection | 15 |
Find the number of times the graphs of f(x) = 1sin(2π(-1x + 5) - 1) - 1 and g(x) = (3x + 3)/(-2x) intersect in the interval [-10, 10]. | 33 | intersection | 22 |
Determine the number of intersection points between the functions f(x) = -1sin(1π(2x^2 - 3x + 2) - 3) + 3 and g(x) = 4x^2 + 2x where -10 ≤ x ≤ 10. | 4 | intersection | 10 |
How many points of intersection exist between the functions f(x) = 3(2sin(2πx - 2) + 2)^2 - 2(2sin(2πx - 2) + 2) + 5 and g(x) = 4x - 1 in the range -10 ≤ x ≤ 10? | 17 | intersection | 15 |
Determine the number of intersection points between the functions f(x) = -1|(-1sin(2πx + 1) + 3) - 3| - 2 and g(x) = -2|x + 2| + 1 where -10 ≤ x ≤ 10. | 4 | intersection | 12 |
Find the number of times the graphs of f(x) = 1(3sin(2πx - 2) + 2) - 1 and g(x) = (2x - 3)/(-1x) intersect in the interval [-10, 10]. | 20 | intersection | 18 |
How many solutions does the equation -2sin(1π(2|x| + 2) - 1) - 3 = (-2x - 3)/(1x + 3) have for x in the interval [-10, 10]? | 31 | intersection | 24 |
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