Calculus Review Test

  1. Which of the following has, as its graph, a parabola opening downwards?
  1. y = x2 – 4x + 7B. y = -x2 + 4x – 1C. (y – 3)2 = (x – 2)2

D. (y – 3) = (x – 2)2

  1. Find cos(θ) if θ lies in the third quadrant and sin(θ) = .
  1. B. C. D.
  1. (x – y)2
  1. x2 – y2B. x2 – xy + y2C. x2 – 2xy + y2D. x2 + 2xy + y2

E. x2(1 – y)2

  1. The period of y = tan
  1. B. C. 2D. 3E. 6
  1. If f(x) = x3 + Ax2 + Bx – 3 and f(1) = 4 and f(-1) = -6, what is the value of

2A + B?

  1. 12B. 8C. 0D. -2E. cannot be

determined

  1. The roots of the equation f(x) = 0 are 1 and -2. The roots of f(2x) = 0 are
  1. 1 and -2B. and -1C. - and 1D. 2 and -4E. -2 and 4
  1. The set of x-intercepts of the graph of f(x) = x3 - 2x2 - x + 2 is
  1. {1}B. {-1,1} C. {1,2}D. {-1,1,2}E. {-1,-2,2}
  1. If f(s) = s2 - 6s + 9, then f(s+3) equals:

A. s2 + 18B. s2 - 65C. s2 + 36D. s2 - 6s +12 E. s2

  1. Which of the following is a reflection of the graph of y = f(x) in the x-axis?
  1. y= -f(x)B. y = f(-x)C. y = |f(x)|D. y = f(|x|)E. y = -f(-x)
  1. The inverse of the function of f(x) = x3 + 2 is
  1. B. (x + 2)3C. (x - 2)3D. E.
  1. If f(x) = x3 - 3x2 - 2x + 5 and g(x) = 2, then g(f(x)) =
  1. 2x3 - 6x2 - 2x + 10B. 2x2 - 6x + 1C. -6

D. -3E. 2

  1. =
  1. B. 2sec2x C. cosxD. tan 2 xE. csc 2 x
  1. What is the period of the function y = 2cos()
  1. 2B. C. 3D. 6πE. π
  1. Solve the following: 2x + 5 < 3x - 7
  1. (-2,∞)B. (12,∞) C. (-∞,12)D. [12,∞)E. (0,∞)
  1. Which of the following defines a function f for which f(-x) = -f(x)?
  1. x2B. sin(x) C. cos(x)D. log(x)E. ex
  1. Which of the following best describes the behavior of the function f(x) = at the values not in its domain?

A. one vertical asymptote, no removable discontinuities

B. two vertical asymptotes

C. two removable discontinuities

D. one removable discontinuity, one vertical asymptote, x=2

E. one removable discontinuity, one vertical asymptote, x=-2

  1. Find tan :
  1. B. C. 1D. E. 0
  1. Which of the following equations has a graph that is symmetric with respect to the origin?
  1. y = B. y = 2x4 + 1C. y = x3 + 2xD. y = x3 + 2

E. y =

  1. Find the equation that passes through the point (5,-3) with a slope of -4.
  1. 5x - 3y = -4B. y + 3 =-4(x - 5)C. y = -4x + 23 D. x - 15y = 20 E. 5x - 3y = 0
  1. The set of zeros of f(x) = x3 + 4x2 + 4x is
  1. {-2}B. {0,-2} C. {0,2}D. {2}E. {2,-2}
  1. An asymptote for
  1. x = 0B. x = -2C. x = 5D. x = -5E. y = -2
  1. The function f(x) = 2x3 + x – 5 has exactly one real zero. It is between
  1. -2 and -1B. -1 and 0C. 0 and 1D. 1 and 2E. 2 and 3
  1. A radioactive substance decays so that half of the substance decays every 2 minutes. If 100 g of the substance are present initially, how many grams will be present after 4 minutes and 8 minutes respectively?
  1. 6.25, 0.390625B. 25, 6.25C. 25, 12.5D. 50, 12.5 E. 50, 25
  1. log5 (25) equals
  1. 0B. 1C. 2D. 1.3979E. 3.1288
  1. ln(x-2) < 0 if and only if
  1. x < 3B. 0 < x < 3C. 2<x<3D. x > 2E. x > 3
  1. If θ is an acute angle and tan(θ) = , then sin(θ) =
  1. B. C. D. E.
  1. If f(x) = x2 + 1 and g(x) = x + 1, then the solution set of f(g(x)) = g(f(x)) is
  1. B. C. all realsD. E. no solution
  1. The set of all points , where t is a real number, is the graph of y =
  1. B. C. D. E. ln x
  1. The values of x for which the graphs of y = x + 2 and y2 = 4x intersect are
  1. -2 and 2B. -2C. 2D. 0E. none of these
  1. Given f(x) = x2 – 4x + 3, then
  1. f(0) =f(-1)B. f(0) = f(2)C. f(0) = f(4)D. f(0) =f (-2)E. f(0) = f(3)
  1. Which of the following is a reflection of the graph y = f(x) in the x-axis?
  1. y = -f(x)B. y = f(-x)C. y = |f(x)|D. y = f(|x|)E. y = -f(x)
  1. If the graph of f(x) = cot(x) is transformed by a horizontal shrink of and a horizontal shift left π, the result is
  1. B.

C. D.

E.

  1. If 3x = 7, which is true?
  1. 7 = logx (3)B. x = log7 (3)C. 3 = logx (7)

D. 7 = log3 (x)E. x = log3 (7)

  1. If f(x) = x3 + Ax2 + Bx – 3 and f(1) = 4 and f(-1) = -6, what is the value of

2A + B?

  1. 12B. 8C. 0D. -2E. cannot be

determined

  1. If f(x) = x3 – 3x2 – 2x + 5 and g(x) = 2, then f(g(x)) =
  1. 2x3 – 6x2 – 2x + 10B. 2x2 – 6x + 1C. -6D. -3

E. 2

  1. Which of the following equations has a graph that is symmetric with respect to the origin?
  1. B. C. D. E.
  1. How many of the following functions are symmetric about the y-axis?

i)ii) iii) y = -5iv) y = x

  1. 0B. 1C. 2D. 3E. 4
  1. Which of the following is not odd?
  1. B. C.

D. E.

  1. If f(x) = x3 + 2x – 1, then f(-2) =
  1. -17B. -13C. -5D. -1E. 3
  1. Let f(x) have an inverse function g(x). Then f(g(x)) =
  1. 1B. xC. D. f(x)g(x)E. none of these
  1. The domain of is
  1. All x except 1B. all except 1 and -1C. all x except -1

D. x ≥ 1E. all reals

  1. If f(x) = x5 – 3x2 + 2x – 7 and g(x) = 3x, then g(f(x)) =
  1. x6 – 9x3 + 2x2 – 7xB. 3x5 – 9x2 + 6x – 21C. 3x

D. 243x5 – 27x3 + 6x – 21E. 3x6 – 9x3 + 6x2 – 21x

  1. The period of is
  1. B. C. D. 3E. 6
  1. (22)(23) + (22)3
  1. 2(25)B. 2(26)C. 211D. 210E. 3(25)
  1. If f(x) = 2x – 8, then f-1(t) =
  1. B. C. D. E.
  1. sin2x – cos2x
  1. 1B. 2sin2x – 1C. (sin x – cos x)2D. 2cos2x – 1

E. tan2x

  1. The domain of is
  1. All x except 0 and 1B. all x except 0 and 1, x ≤ 2C. x ≤ 2

E. x > 2

  1. The distance between the points (-5,2) and (5,-3)
  1. 125B. 5C. D. E. 1
  1. If and g(x) = 2x, then the solution set of f(g(x)) = g(f(x) is
  1. B. C. D. E.
  1. Find the equation of the line that passes through (5,-3) with a slope of -4.
  1. 5x – 3y = -4B. y + 3 = -4(x – 5)C. y = -4x + 23

D. x – 15y = 20E. 5x – 3y = 0

  1. The function whose graph is a reflection in the y-axis of the graph of f(x) = 1 – 3x is
  1. B. C.

D. E.

  1. Which of the following functions is periodic with period π?
  1. B. C. D.

E.

  1. arcsin()
  1. B. C. D. E.
  1. How many of the following functions have the property f(x) = f(-x)?

i)f(x) = x4 + x2ii) f(x) = cos xiii) f(x) = 4x

iv) f(x) = 17