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: \( 9^{\log_{9}(4)} = \)
A. 3
B. 4
C. 9
D. 81

Question 2

Simplify: \( 3^{\log_{3}(-5)} = \)
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. \( \dfrac{8}{39} \)
B. -3
C. 3
D. 32

Question 5

If \( \log_{x}(3) = \dfrac{1}{4} \), then \( x = \)
A. 81
B. \( \dfrac{1}{81} \)
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. \( \dfrac{2}{3} \)
B. \( \dfrac{(2 + e)}{3} \)
C. \( \dfrac{3}{2} \)
D. \( \dfrac{e}{3} \)

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. \( (-\infty , -2) \)
B. \( (-\infty , +\infty) \)
C. \( (-2; , +\infty) \)
D. \( (-\infty , +2) \)

Question 12

If \( f(x) = \dfrac{\sqrt{x - 1}}{x^{2} - 9} \), then the domain of \( f \) is given by the interval
A. \( (1 , +\infty) \)
B. \( (-3 , +3) \)
C. \( [1 , 3) \cup (3 , +\infty) \)
D. \( (-3 , 3) \cup (3 , +\infty) \)

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, \( \sqrt{x^{2} -4x + 4} = \)
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. \( \dfrac{3}{2x} \)
B. \( \dfrac{3x}{2} \)
C. \( 1 + \dfrac{1}{x} \)
D. \( \dfrac{3}{2} - \dfrac{1}{x} \)

Question 18

If \( f(x) = \dfrac{x - 1}{x + 2} \), then the range of \( f \) is given by the interval
A. \( (-\infty , -2) \cup (-2 , +\infty) \)
B. \( (-\infty , 1) \cup (1 , +\infty) \)
C. \( (-2; , +\infty) \)
D. \( (-\infty , 1) \)

Question 19

\( \ln((x - 1)^{2}) = 2 \ln(x - 1) \) for all \( x \) in the interval
A. \( (-\infty , +\infty) \)
B. \( [0 , +\infty) \)
C. \( (-\infty , 1) \cup (1 , +\infty) \)
D. \( (1 , +\infty) \)

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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