College Algebra Questions With Answers
Sample 1

College algebra multiple choice questions, with answers, are presented. The solutions are at the bottom of the page. Also Detailed solutions with full explanations are included.

  1. Simplify: 9log9(4) =
    A. 3
    B. 4
    C. 9
    D. 81
  2. Simplify: 3log3(-5) =
    A. -5
    B. 3
    C. 9
    D. undefined
  3. If f(x) = -2x2 + 8x - 4, which of the follwoing is true?
    A. The maximum value of f(x) is - 4.
    B. The graph of f opens upward.
    C. The graph of f has no x-intercept
    D. f is not a one to one function.
  4. If f(x) = 5 - 2x, then f-1(- 3) =
    A. 8/39
    B. -3
    C. 3
    D. 32
  5. If logx(3) = 1/4, then x =
    A. 81
    B. 1/81
    C. 3
    D. 9
  6. If f(x) = -x2 + 1, then f(x + 1) =
    A. -x2 + 1
    B. -x2 - 2x
    C. -x2
    D. -x2 -2x - 2
  7. If f(x) = x - 4, then (fof)(3) = =
    A. 1
    B. -1
    C. -5
    D. 5
  8. If ln(3x - 2) = 1, then x =
    A. 2/3
    B. (2 + e)/3
    C. 3/2
    D. e/3
  9. The number of solutions of (x2 + 1)2 + 2(x2 + 1) - 3 = 0 is equal to
    A. 1
    B. 2
    C. 3
    D. 4
  10. If the graph of y = (x - 2)2 - 3 is translated 5 units up and 2 units to the right, then the equation of the graph obtained is given by
    A. y = x2 + 2
    B. y = (x - 2)2 + 5
    C. y = (x + 2)2 + 2
    D. y = (x - 4)2 + 2
  11. If f(x) = -ex - 2, then the range of f is given by the interval
    A. (-∞ , -2)
    B. (-∞ , +∞)
    C. (-2; , +∞)
    D. (-∞ , +2)
  12. If f(x) = √(x - 1) / (x2 - 9), then the domain of f is given by the interval
    A. (1 , +∞)
    B. (-3 , +3)
    C. [1 , 3)U(3 , +∞)
    D. (-3 , 3)U(3 , +∞)
  13. The number of points of intersections of the graphs of y = 2x and y = -x2 + 2 is equal to
    A. 0
    B. 1
    C. 2
    D. 3
  14. If f(x) = ln(x + 1) - 2, then f-1(x) =
    A. ex + 1 - 2
    B. ex - 2
    C. ex + 2 - 2
    D. ex + 2 - 1
  15. For all x real, √(x2 -4x + 4) =
    A. x - 2
    B. x + 2x + 2
    C. |x - 2|
    D. x + 2
  16. The value of x that makes x2 + 6x + 13 maximum is equal to
    A. 6
    B. -3
    C. 13
    D. 3
  17. eln(3) - ln(2) + ln(1/x) =
    A. 3 / (2x)
    B. 3x/2
    C. 1 + 1/x
    D. 3/2 - 1/x
  18. If f(x) = (x - 1) / (x + 2), then the range of f is given by the interval
    A. (-∞ , -2)U(-2 , +∞)
    B. (-∞ , 1)U(1 , +∞)
    C. (-2; , +∞)
    D. (-∞ , 1)
  19. ln((x - 1)2) = 2 ln(x - 1) for all x in the interval
    A. (-∞ , +∞)
    B. [0 , +∞)
    C. (-∞ , 1)U(1 , +∞)
    D. (1 , +∞)
  20. Let f(x) = x2 + 2x + 4. Which of the following statements is NOT true?
    A. f(x) has a maximum value
    B. The graph of f is not a line
    C. The graph of f has no x-intercepts.
    D. The graph of f has a y-intercept.

Answers to the Above Questions

  1. B
  2. D
  3. D
  4. C
  5. A
  6. B
  7. C
  8. B
  9. A
  10. D
  11. A
  12. C
  13. C
  14. D
  15. C
  16. B
  17. A
  18. B
  19. D
  20. A

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