College Algebra Questions With Answers
Sample 1

A set of college algebra multiple choice questions, with answers, are presented. The answers are at the bottom of the page. Also Detailed solutions with full explanations are included.
  1. 9log9(4) =

    A. 3 B. 4 C. 9 D. 81

  2. 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.

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