College Algebra Questions With Answers
Sample 2

A set of college algebra multiple choice questions, with answers, are presented. The answers are at the bottom of the page.

Questions

Question 1

How many x intercepts does the graph of the function \( f(x) = x^{3} + 4 \) have?

A. 0
B. 1
C. 2
D. 3

Question 2

If \( \log_{b}(5) = c \), then \( b^{4c} = \)

A. 4
B. 5
C. 25
D. 625

Question 3

How many points of intersection do the graphs of the functions \( f(x) = x^{2} \) and \( g(x) = 2^{x} \) have?

A. 1
B. 2
C. 3
D. 4

Question 4

The range of the function \( f(x) = -x^{2} + 2x - 5 \) is given by

A. \( (0 , \infty) \)
B. \( (-\infty , 4]\)
C. \( (-\infty , - 4] \)
D. \( (- \infty , - 5] \)

Question 5

Which of these functions does not have an inverse?

A. \( f(x) = |x - 5| \)
B. \( h(x) = 2x - 9 \)
C. \( k(x) = \ln(- x + 4) \)
D. \( j(x) = x^{1/3} \)

Question 6

The solution set of the inequality \( (x + 5)^{4}(x + 3) \geq 0 \) is given by interval

A. \( [- 3 , \infty) \)
B.\( \{- 5\} U [- 3 , \infty) \)
C. \( (- \infty , \infty) \)
D. \( (- 3 , \infty) \)

Question 7

The range of the function \( h(x) = -|x - 5| - 2 \) is given by

A. \( (- \infty , 0) \)
B. \( (- \infty , - 2) \)
C. \( (-\infty , -2] \)
D. \( (- \infty , 2] \)

Question 8

\( 5 \ln e^{2} - 2 \ln (7e) + \ln 49 = \)

A. 8
B. 3
C. \( 4 \ln 7 \)
D. \( 8 e - 4 \ln 7 \)

Question 9

If \( f(x) = \dfrac{x}{(- x + 4)} \) and \( g(x) = 2x + 2 \), then \( (f_{o} g)(1) = \)

A. \( \dfrac{4}{3} \)
B. \( 4 \dfrac {1}{3} \)
C. 4
D. undefined

Question 10

\( \sqrt{x^{2} + 6x + 9} = \)

A. \( x + \sqrt{6x} + 3\)
B. \( x + 3\)
C. \( |x + 3| \)
D. \( (x + 3)^{2} \)

Question 11

If \( f(x) = x^{2} + 1 \) for \( x \leq 0 \), then \( f^{ -1}(x) = \)

A. \( x -1 \)
B. \( \sqrt{x - 1} \)
C. \( \sqrt{x + 1} \)
D. - \( \sqrt{x - 1} \)

Question 12

The domain of \( f(x) = \ln(2 - x) + \ln(3 - x) \) is given by

A. \( (-\infty , 2) \)
B. \( (2 , 3) \)
C. \( (-\infty , 3) \)
D. \( (-\infty , 2] \)

Question 13

The solution set of the inequality \( (x - 1)^{2} \leq 0 \) is given by

A. \( (-\infty , \infty) \)
B. \( (-\infty , 1] \)
C. \( \{1\} \)
D. \( [1 , \infty) \)

Question 14

The solution to the equation \( 2 (4^{x+1}) = 4 (8^{x + 2}) \)

A. -5
B. 1
C. 0
D. no solution

Question 15

The number of solutions of the equation \( | - x^{2} + 4x + 1 | = 5 \) is equal to

A. 1
B. 2
C. 3
D. 4

Question 16

Using the absolute value concept, the statement
The distance from x to -6 is not less than 7 may be written as follows

A. \( |x + 6| \geq 7 \)
B. \( |x + 6| > 7 \)
C. \( |x + 7| \geq -6 \)
D. \( |x + 7| \geq 6 \)

Question 17

If \( f(2x + 3) = 2x - 1 \), then \( f(3x + 4) = \)

A. 6x + 7
B. 3x
C. 6x + 11
D. 9x + 15

Question 18

\( -x^{2} + x - 3 = \)

A. -\((x + \dfrac{1}{2})^{2} - \dfrac{11}{4}\)
B. \((x - \dfrac{1}{2})^{2} - \dfrac{11}{4}\)
C. -\((x - \dfrac{1}{2})^{2} - \dfrac{11}{4}\)
D. -\((x - \dfrac{1}{2})^{2} + \dfrac{11}{4}\)

Question 19

How many solutions do the equation \( \dfrac{1}{x} + \dfrac{1}{(x + 1)} = \dfrac{1}{3} \) have?

A. 0
B. 1
C. 2
D. 3

Question 20

If the whole graph of function \( f \) lies in quadrant IV, then the graph of the inverse of \( f \) lies in quadrant

A. I
B. II
C. III
D. IV

Answers to the Above Questions

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

More References and links

Algebra Questions and problems
More ACT, SAT and Compass practice