## Calculus. There are 70 multiple choice questions and 5 short free response questions

1. Which of the following relations are functions?

I.y = -x + 3
II.x = y + 3
III.x – y = 3

 ·         None of them ·         All of them ·         Choice II only ·         Choice III only

2. Find the range for f(x) = -x2 + 1, for x > 0.
 ·         y > 1 ·         y ≥ 1 ·         y < 1 ·         y ≤ 1

3. Find the domain for .
 ·         x ≠ 2 ·         x ≠ -3 ·         x ≠ -3, -2 ·         x ≠ -2

4. Find the range of the function:

f(x) = x + 3, for x ≠ 1.

 ·         All real numbers ·         y ≠ 4 ·         y ≠ 3 ·         y ≠ 1

5. Determine whether f(x) = -5x2 + 3x + 4 has a maximum or minimum.
 ·         Maximum ·         Minimum

6. Where is the function 4(x + 4)(x – 6)3 > 0?
 ·         For x > -4 or x < 6 ·         For x < -4 or x > 6 ·         For no x values ·         For all x values

7. For which x value would the graph of y = x2 – 25 be below the x-axis?

 ·         7 ·         6 ·         5 ·         4

8. Find f(g(5)) if  and g(x) = (x-1)2.

 · · · ·         24

9. Find f[g(x)] if f(x) = x2 + 1 and g(x) = x5.
 ·         (x5 + 1)2 ·         (x2 + 1)5 ·         x10 + 1 ·         None of these

10. Find g(x) if g(x) is the resulting function from moving f(x) = (x + 2) right 1 unit and up 6 units.

 ·         g(x) = (x + 1) + 6 ·         g(x) = (x – 1) + 6 ·         g(x) = (x + 3) + 6 ·         g(x) = (x – 6) + 1

11. Rewrite f(x) = sin(x) if the function is stretched vertically by a factor of 2.
 ·         sin(2x) · · ·         2sin(x)

12. What is the domain of ?
 ·         All real numbers except 2 ·         All real numbers less than 2 ·         All real numbers greater than 4 ·         All real numbers greater than 2 ·         All real numbers

13. Find the range of .
 ·         y > 4 ·         y ≥ 0 ·         y > 0 ·         All real numbers

14. Is the function of  even, odd, or neither?
 ·         Even ·         Odd ·         Neither

15. Find the period and amplitude for f(x) = 3sin(4x).

 ·         Amplitude = 4, Period = ·         Amplitude = 3, Period = 8π ·         Amplitude = , Period = ·         Amplitude = 3, Period =
16. Determine the domain of the function.

 ·         All real numbers ·         x > 1 ·         x ≤ 1 ·         All real numbers except 1

17. Determine the domain of the function.

 ·         All real numbers except -8, -3, and 2 ·         x ≥ 0 ·         All real numbers ·         x ≥ -3, x ≠ 2

18. f(x) = 3x + 2; g(x) = 3x – 5

Find f/g.

 ·         (f/g)(x) =  ; domain {x|x ≠ – } ·         (f/g)(x) =  ; domain {x|x ≠ } ·         (f/g)(x) = ; domain {x|x ≠ } ·         (f/g)(x) =  ; domain {x|x ≠ – }

19. Use your graphing calculator to graph f(x) = |x + 1| and determine where the function is increasing and decreasing.

 ·         Increasing x > -1; Decreasing x < -1 ·         Increasing x < 1; Decreasing x > 1 ·         Increasing x < -1, Decreasing x > -1 ·         Increasing x > 1; Decreasing x < 1

20. Select true or false:

The function -3(x + 2)(x – 5)3 > 0, when x < -2 or x > 5.

 ·         True ·         False

21. f(x) = 2x + 6, g(x) = 4x2

Find (f + g)(x).

 ·         8x3 + 24x · ·         4x2 + 2x + 6 ·         -4x2 + 2x + 6

22. f(x) = ; g(x) = 8x – 12

Find f(g(x)).

 ·         f(g(x)) = 2 ·         f(g(x)) = 8 – 12 ·         f(g(x)) = 2 ·         f(g(x)) = 8

23. Describe how the graph of y = x2 can be transformed to the graph of the given equation:

y = x2 – 20

 ·         Shift the graph of y = x2 left 20 units. ·         Shift the graph of y = x2 up 20 units. ·         Shift the graph of y = x2 down 20 units. ·         Shift the graph of y = x2 right 20 units.

24. Is the function of f(x) = |4x| +  even, odd, or neither?

 ·         Even ·         Odd ·         Neither

25. State the domain of the rational function.

f(x) =

 ·         All real numbers except -10 and 10 ·         All real numbers except 13 ·         All real numbers except 10 ·         All real numbers except -13 and 13

26. Use your graphing calculator to evaluate .
 ·         0 ·         π ·         1 ·         e4 ·

27. Use your calculator to select the best answer below:

 ·         does not exist ·         1 ·         -1 ·         0

28.

 · · · ·         0

29. Find .

 ·         Does not exist ·         4 ·         3 ·         0

30. If  and , then find .

 ·         64 ·         -4 ·         16 ·         28

31. Evaluate .

 ·         0 ·         does not exist ·         1 ·         -1

32. Evaluate .

 ·         0 ·         25 · ·

33. Evaluate .

 ·         1 · · ·         Does not exist

34. If f is a continuous function with odd symmetry and, which of the following statements must be true?

I.
II.There are no vertical asymptotes.
III.The lines y = 6 and y = -6 are horizontal asymptotes.

 ·         All statements are true. ·         I only ·         II only ·         III only

35. What are the horizontal asymptotes of the function ?

 ·         y = -2 and y = 2 ·         y = 2 only ·         y = -2 only ·         y = 0

36. Which one or ones of the following statements is/are true?

I.If the line y = 2 is a horizontal asymptote of y = f(x), then f is not defined at y = 2.
II.If f(1) > 0 and f(3) < 0, then there exists a number c between 1 and 3 such that f(c) = 0.
III.If f is continuous at x = 6 and f(6) = 8 and f(4) = 2, then

 ·         All statements are true. ·         I only ·         II only ·         III only

37. Find .

 · ·         0 ·         −∞ ·         ∞

38. Evaluate .
 ·         1 ·         0 ·         3 ·         does not exist

39. Which of the following are the equations of all horizontal and vertical asymptotes for the graph of ?

 ·         y = 0, x = -4, x = 4 ·         y = 1, x = -4, x = 4 ·         y = 0, x = -4, x = 0, x = 4 ·         y = 1, x = -4, x = 0, x = 4

40. Evaluate .

 ·         does not exist ·         3 ·         8 ·         1

41. Where is  discontinuous?
 ·         x = 4 and x = 5 ·         x = 4 ·         x = 5 ·         f(x) is continuous everywhere

42. Which of the following are continuous for all real values of x?

I.
II.
III.

 ·         I only ·         II only ·         I and II only ·         I and III only

43. Which of the following must be true for the graph of the function?

There is:

I.a removable discontinuity at x = 5
II.a vertical asymptote at x = 5
III.an infinite discontinuity at x = 5

 ·         I only ·         II only ·         III only ·         I, II, III

44. What is the average rate of change of y with respect to x over the interval [-1, 2] for the function y = 3x + 2?

 ·         1 ·         3 · ·         9

45. What is the instantaneous slope of y =  at x = 3?

 · · · ·

46. The height, s, of a ball thrown straight down with initial speed 32 ft/sec from a cliff 128 feet high is s(t) = -16t2 – 32t + 128, where t is the time elapsed that the ball is in the air. What is the instantaneous velocity of the ball when it hits the ground?
 ·         -96 ft/sec ·         256 ft/sec ·         0 ft/sec ·         112 ft/sec

47. The surface area of a right circular cylinder of height 5 feet and radius r feet is given by S(r)=2πrh+2πr2. Find the instantaneous rate of change of the surface area with respect to the radius, r, when r = 6.

 ·         24π ·         34π ·         64π ·         20π ·
48. If  and , then .

 ·         True ·         False

49. Find the limit of the function algebraically.

 ·         Does not exist ·         7 ·         0 ·         -7

50. Find .

 ·         10 ·         18 ·         Does not exist ·         10 or 18

51. Evaluate .
 ·         0 ·         −∞ ·         ∞ ·         Does not exist

52. Evaluate .
 ·         1 ·         0 · ·         Does not exist

53. Evaluate

 ·         ∞ ·         -∞ ·         0 ·

54. Find the equation of the horizontal asymptote for the function,  .

 ·         There is no horizontal asymptote. ·         y = 0 ·         y = 1 ·         y = x

55. Which of the following is false for  ?

 ·         The x-axis is an asymptote of f(x). ·         x = -1 is not an asymptote of f(x). ·         x = 1 is an asymptote of f(x). ·         The y-axis is an asymptote of f(x).
56. To two decimal places, find the value of k that will make the function f(x) continuous everywhere.

 ·         11.00 ·         -2.47 ·         -0.47 ·         None of these

57. Where is  discontinuous?

 ·         f(x) is continuous everywhere ·         1 ·         1, 4 ·         4

58. Is the function  continuous?

 ·         Yes ·         No

59. List the discontinuities for the function f(x) = cot(  ).

 ·         There are no discontinuities. ·         n(  ), where n is an integer ·         n(  ), where n is an integer ·         n(  ), where n is an integer

60. Which of the following is true for  ?

 ·         There is a removable discontinuity at x = 3. ·         There is a non-removable discontinuity at x = 3. ·         The function is continuous for all real numbers.
61. What is the instantaneous slope of y =  at x = 5?

 · ·         1 ·         -1 ·

62. What is the average rate of change of y with respect to x over the interval [-2, 6] for the function y = 5x + 2?

 ·         5 ·         2 · ·         10

63. What is the slope for the function y = -3x2 + 2 at the point x = 2?

 ·         -4 ·         -10 ·         -12 ·         The slope cannot be determined.

64. The surface area, S, of a sphere of radius r feet is S = S(r) = 4πr2. Find the instantaneous rate of change of the surface area with respect to the radius r at r = 4.

 ·         32π ·         16π ·         64π ·         4π

65. A ball is thrown vertically upward from the top of a 100 foot tower, with an initial velocity of 10 ft/sec. Its position function is s(t) = -16t2 + 10t + 100. What is its velocity in ft/sec when t = 2 seconds?

 ·         -32 ·         -38 ·         -54 ·         80

66. Using the graph of f(x) below, find .

 ·         −5 ·         −∞ ·         0 ·         1.7

67. Find .

 ·         Does not exist ·         0 · ·

68. What is ?

 ·         ∞ ·         0 ·         −4 ·         −∞

69. What is ?
 ·         −6 ·         0 ·         1 ·         Does not exist

70. Find the limit of the function by using direct substitution.

 ·         Does not exist ·         0 ·         5 ·         -5
71. State the domain and range for the function f(x) = -x2 + 5.
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 72. Show that the function f(x) = x-4 + cos(-2x) is even, odd, or neither. _____________________________

 73. Determine the equation of a line, in slope-intercept form, that passes through the points (5, 6) and (10, 2). ____________________________

 74. Write the equation of the function g(x) if g(x) = f(x – 3) +1 and f(x) = x3 + 1. _____________________________ 75. Identify the maximum and minimum values of the function y = 8 cos x in the interval [-2π, 2π]. Use your understanding of transformations, not your graphing calculator.

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