Inverse functions and graphs of simple functions - Question Bank

1. The graph of y = x⁴ is flatter than the graph of y = x² near the origin.
A) True
B) False
C) Depends on the value of x
D) Only true for x > 1
2. If f(x) = x + 1, what is f⁻¹(x)?
A) x - 1
B) 1 - x
C) 1/x
D) x
3. The graph of y = tan⁻¹(x) has horizontal asymptotes at:
A) y = 0 and y = π
B) y = -π/2 and y = π/2
C) y = -π and y = π
D) y = 1 and y = -1
4. What is the range of the function f(x) = arcsin(x) + arccos(x)?
A) [0, π]
B) [0, π/2]
C) [π/2, π]
D) {π/2}
5. The graph of y = x² - 1 is a translation of y = x² by:
A) 1 unit up
B) 1 unit down
C) 1 unit left
D) 1 unit right
6. Which function's graph passes through the origin?
A) f(x) = 1/x
B) f(x) = e^x
C) f(x) = x³
D) f(x) = log(x)
7. What is the domain of the inverse function of f(x) = log₂(x)?
A) (-∞, ∞)
B) (0, ∞)
C) [0, ∞)
D) (-1, 1)
8. The graph of y = 1/(x-a) is a translation of y = 1/x by 'a' units in the:
A) Positive y-direction
B) Negative y-direction
C) Positive x-direction
D) Negative x-direction
9. The function f(x) = x|x| is:
A) Even
B) Odd
C) Neither even nor odd
D) Both even and odd
10. What is the value of arccot(-1)?
A) π/4
B) 3π/4
C) 5π/4
D) -π/4
11. The graph of y = ln(x) is the reflection of y = e^x across:
A) The x-axis
B) The y-axis
C) The origin
D) The line y = x
12. What is the range of f(x) = 3 + arctan(x)?
A) [3, 3+π]
B) (3-π/2, 3+π/2)
C) [0, π]
D) (-∞, ∞)
13. What is the domain of f(x) = arcsin(2x)?
A) (-∞, ∞)
B) [-1, 1]
C) [-1/2, 1/2]
D) (0, 1)
14. The graph of y = x^n for even integer n > 1 is similar to the graph of:
A) y = x³
B) y = x²
C) y = x
D) y = 1/x
15. The graph of y = x^n for odd integer n > 1 is similar to the graph of:
A) y = x²
B) y = x³
C) y = |x|
D) y = 1/x
16. If f(x) = x, what is f⁻¹(x)?
A) -x
B) 1/x
C) x
D) 0
17. What is the range of f(x) = csc(x)?
A) (-1, 1)
B) [-1, 1]
C) (-∞, -1] ∪ [1, ∞)
D) [1, ∞)
18. What is the domain of f(x) = tan(x)?
A) (-∞, ∞)
B) R - {nπ | n ∈ Z}
C) R - {(2n+1)π/2 | n ∈ Z}
D) (-π/2, π/2)
19. The graph of y = 1/x is symmetric with respect to:
A) The x-axis
B) The y-axis
C) The origin
D) The line y = x and the origin
20. What is the value of arctan(-√3)?
A) π/3
B) -π/3
C) π/6
D) -π/6
21. What is the value of arccos(-1)?
A) 0
B) π/2
C) π
D) 3π/2
22. What is the value of arcsin(-1/2)?
A) π/6
B) -π/6
C) π/3
D) -π/3
23. The graph of y = -x³ is symmetric with respect to:
A) The x-axis
B) The y-axis
C) The origin
D) The line y = x
24. What is the domain of the function f(x) = log(x²)?
A) (-∞, ∞)
B) [0, ∞)
C) (0, ∞)
D) R - {0}
25. The graph of y = √(-x) is a reflection of the graph of y = √x across:
A) The x-axis
B) The y-axis
C) The origin
D) The line y = x
26. If f(x) = a^x where a > 0 and a ≠ 1, its inverse function f⁻¹(x) is:
A) log_a(x)
B) log_x(a)
C) x^a
D) a/x
27. What is the principal value range of arccsc(x)?
A) [-π/2, 0) ∪ (0, π/2]
B) [0, π] - {0}
C) (-π/2, π/2) - {0}
D) [0, π]
28. What is the principal value range of arcsec(x)?
A) [0, π] - {π/2}
B) [0, π/2] ∪ [π/2, π]
C) [0, π]
D) (-π/2, π/2) - {0}
29. The graph of y = 1/x² is symmetric with respect to:
A) The x-axis
B) The y-axis
C) The origin
D) The line y = x
30. What is the range of f(x) = sec(x)?
A) (-1, 1)
B) [-1, 1]
C) (-∞, -1] ∪ [1, ∞)
D) [1, ∞)
31. What is the domain of f(x) = cot(x)?
A) (-∞, ∞)
B) R - {nπ | n ∈ Z}
C) R - {(2n+1)π/2 | n ∈ Z}
D) (0, π)
32. The graph of y = c (where c is a constant) is a:
A) Vertical line
B) Horizontal line
C) Parabola
D) Hyperbola
33. If f(x) = log_b(x), its inverse function f⁻¹(x) is:
A) b^x
B) x^b
C) log_x(b)
D) 1/log_b(x)
34. What is the value of arctan(1)?
A) 0
B) π/4
C) π/3
D) π/2
35. What is the value of arccos(0)?
A) 0
B) π/4
C) π/2
D) π
36. What is the value of arcsin(1/2)?
A) π/6
B) π/4
C) π/3
D) π/2
37. Which of the following is NOT an even function?
A) f(x) = x²
B) f(x) = cos(x)
C) f(x) = |x|
D) f(x) = x³
38. Which of the following is NOT an odd function?
A) f(x) = x³
B) f(x) = sin(x)
C) f(x) = x
D) f(x) = x²
39. The graph of y = x² is symmetric with respect to:
A) The x-axis
B) The y-axis
C) The origin
D) The line y = -x
40. What is the domain of the function f(x) = log_b(x) where b > 1?
A) (-∞, ∞)
B) [0, ∞)
C) (0, ∞)
D) (-∞, 0)
41. The range of the function f(x) = sin(x) is:
A) [0, π]
B) [-1, 1]
C) (-∞, ∞)
D) [0, 1]
42. What is the domain of the function f(x) = √x?
A) (-∞, ∞)
B) [0, ∞)
C) (0, ∞)
D) (-∞, 0]
43. The graph of y = |x| has a minimum value at:
A) x = -1
B) x = 1
C) x = 0
D) All x
44. If f(x) = 1/x, what is its inverse function, f⁻¹(x)?
A) 1/x
B) -1/x
C) x
D) 1/(x-1)
45. The graph of y = x³ is symmetric with respect to:
A) The x-axis
B) The y-axis
C) The origin
D) The line y = x
46. What is the domain of the inverse function of f(x) = e^x?
A) (-∞, ∞)
B) (0, ∞)
C) [0, ∞)
D) (-1, 1)
47. If f(x) = 2^x, what is its inverse function, f⁻¹(x)?
A) -2^x
B) log₂(x)
C) x/2
D) log₁₀(x)
48. What is the principal value range of the inverse trigonometric function arccot(x)?
A) (0, π)
B) [0, π]
C) (-π/2, π/2)
D) [0, π/2]
49. The function f(x) = arctan(x) is defined for all real numbers. What is its range?
A) [0, π]
B) (-π/2, π/2)
C) [0, π/2]
D) (-∞, ∞)
50. What is the range of the function f(x) = arccos(x)?
A) [0, π]
B) (-π/2, π/2)
C) [0, π/2]
D) (-∞, ∞)
All Question Banks
E-Book Inverse functions and graphs of simple functions One Line Questions Inverse functions and graphs of simple functions Online Test Inverse functions and graphs of simple functions