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.


Question 1

Simplify: 9 log9(4) =
A. 3
B. 4
C. 9
D. 81

Question 2

Simplify: 3 log3(-5) =
A. -5
B. 3
C. 9
D. undefined

Question 3

If f(x) = -2x 2 + 8x - 4, which of the following 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.

Question 4

If f(x) = 5 - 2 x , then f -1 (- 3) =
A. 8/39
B. -3
C. 3
D. 32

Question 5

If log x (3) = 1/4, then x =
A. 81
B. 1/81
C. 3
D. 9

Question 6

If f(x) = -x 2 + 1, then f(x + 1) =
A. -x 2 + 1
B. -x 2 - 2x
C. -x 2
D. -x 2 -2x - 2

Question 7

If f(x) = x - 4, then (f o f)(3) = =
A. 1
B. -1
C. -5
D. 5

Question 8

If ln(3x - 2) = 1, then x =
A. 2/3
B. (2 + e)/3
C. 3/2
D. e/3

Question 9

The number of solutions of (x 2 + 1) 2 + 2(x 2 + 1) - 3 = 0 is equal to
A. 1
B. 2
C. 3
D. 4

Question 1o

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 = x 2 + 2
B. y = (x - 2) 2 + 5
C. y = (x + 2) 2 + 2
D. y = (x - 4) 2 + 2

Question 11

If f(x) = -e x - 2, then the range of f is given by the interval
A. (-∞ , -2)
B. (-∞ , +∞)
C. (-2; , +∞)
D. (-∞ , +2)

Question 12

If f(x) = √(x - 1) / (x 2 - 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 , +∞)

Question 13

The number of points of intersections of the graphs of y = 2 x and y = -x 2 + 2 is equal to
A. 0
B. 1
C. 2
D. 3

Question 14

If f(x) = ln(x + 1) - 2, then f -1 (x) =
A. e x + 1 - 2
B. e x - 2
C. e x + 2 - 2
D. e x + 2 - 1

Question 15

For all x real, √(x 2 -4x + 4) =
A. x - 2
B. x + 2x + 2
C. |x - 2|
D. x + 2

Question 16

The value of x that makes x 2 + 6x + 13 maximum is equal to
A. 6
B. -3
C. 13
D. 3

Question 17

e ln(3) - ln(2) + ln(1/x) =
A. 3 / (2x)
B. 3x/2
C. 1 + 1/x
D. 3/2 - 1/x

Question 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)

Question 19

ln((x - 1) 2 ) = 2 ln(x - 1) for all x in the interval
A. (-∞ , +∞)
B. [0 , +∞)
C. (-∞ , 1)U(1 , +∞)
D. (1 , +∞)

Question 20

Let f(x) = x 2 + 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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