# 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.

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