# 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.