# 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

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