Question 1

Which of the following is the correct domain of the function $$f(x) = \sqrt{12 - 2x}$$?

Accepted Answer

$$x \leq 6$$

Question 2

Find the slope of the line passing through the points $$\left(-\frac{3}{4}, -\frac{1}{4}\right)$$ and $$\left(\frac{5}{7}, -\frac{5}{7}\right).$$

Accepted Answer

$$-1$$

Question 3

What is the $$y-$$intercept of the line $$3x - 4y = 20$$?

Accepted Answer

$$(0, -5)$$

Question 4

Given the function $$f(x) = |1 - 6 - 4x|$$, which of the following is equivalent to $$f(x)$$?

Accepted Answer

$$| -5 - 4x |$$

Question 5

Solve for $$x$$: $$3x - 5 = 2x + 1.$$

Accepted Answer

$$x = 1$$

Question 6

If $$f(x) = x^5$ - 2$$ and $$g(x) = \sqrt{x + 2}$$, what is the domain of $$g \circ f$$?

Accepted Answer

$$x^5 - 2$$ \geq -2$$

Question 7

A taxi fare in Boulder City is $$4.30 to get in, plus 2.40 $$per mile. If David's taxi ride costs $30.90, how far did he travel?

Accepted Answer

$$12$$ miles

Question 8

Diane is planning a rectangular farm of donkeys with its length twice its width. The perimeter is $$45$$ meters. What are the dimensions of the farm?

Accepted Answer

Length $$= 15 m$$, Width $$= 7.5 m$$

Question 9

Deisy worked 48 hours at a store and earned a $$700$$ paycheck. She earns time and a half (1.5 times her regular hourly wage) for the number of hours she works in excess of $$40. $$What is Deisy's regular hourly wage?

Accepted Answer

$$12.50$$

Question 10

Given the piecewise function $$h(x) = \begin{cases} -3x - 18 & 	ext{for } x \u003c -5 \ 1 & 	ext{for } -5 \leq x \u003c 1 \ x + 2 & 	ext{for } x \geq 1 \end{cases}$$, what is $$h(4)$$?

Accepted Answer

$$6$$

Question 11

Which of the following is NOT a function?

Accepted Answer

$$f(x) = \pm \sqrt{x}$$

Question 12

Find the $$x-$$intercept of the line $$3x - 4y = 20.$$

Accepted Answer

$$(\frac{20}{3}, 0)$$

Question 13

If $$f(x) = x^5$ - 2$$ and $$g(x) = \sqrt{x + 2}$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$(\sqrt{x + 2})^5$ - 2$$

Question 14

Given the equation $$5x - 3y = -15$$, what is the slope of the line?

Accepted Answer

Question 15

Solve for $$x$$: $$3(x + 1) = 5 - 2(3x + 4).$$

Accepted Answer

$$x = -3$$

Question 16

If $$g(x) is $$the function shown in the graph with $$g(0) = -4$$, $$g(-2) = 2$$, and $$g(2.4) = -2.6176$$, which of the following is true?

Accepted Answer

$$g(0) = -4$$

Question 17

Which of the following best describes the graph of $$y = 2x + 1$$?

Accepted Answer

A line with slope $$2$$ and $$y-$$intercept $$1$$

Question 18

Which of the following is the correct solution to $$5x - 2 + 3x = 2x + 6 - 4x$$?

Accepted Answer

$$x = -1$$

Question 19

Given $$f(x) = x^4$ - \sqrt{3x} + \frac{3}{\sqrt{3}}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$x \geq 0$$

Question 20

Which of the following is the correct $$y-$$intercept for the line $$2x + y = 4$$?

Accepted Answer

$$(0, 4)$$

College Algebra: Sample Exam 1 Study Guide

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