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.
_____________________________

 

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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