# 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 intervalA. (-∞ , -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

- B
- D
- D
- C
- A

- B
- C
- B
- A
- D

- A
- C
- C
- D
- C

- B
- A
- B
- D
- A

### More References and links

Algebra Questions and problemsMore ACT, SAT and Compass practice