Question 1

Which of the following sets is the domain of the relation $$\{(0, 9.1), (10, 6.7), (20, 10.7), (30, 13.2), (40, 21.2)\}$$?

Accepted Answer

$$\{0, 10, 20, 30, 40\}$$

Question 2

Given the relation $$\{(2, 3), (2, 5), (4, 7)\}$$, is this relation a function?

Accepted Answer

No, because the x-value 2 is paired with two different y-values.

Question 3

Does the equation $$y^2 = 1$$ - $$x^2$$ define $$y as a $$function of $$x$$?

Accepted Answer

No, because for some $$x$$ there are two possible values of $$y.$$

Question 4

Which of the following best describes the vertical line test for functions?

Accepted Answer

If any vertical line intersects the graph in more than one point, the graph does not define $$y as a $$function of $$x.$$

Question 5

Given the function $$f(x) = 2x - 3$$, what is $$f(-2)$$?

Accepted Answer

$$-7$$

Question 6

A function $$f is $$defined on the interval $$[-2, 1]$$ and its range is $$[0, 3]. $$Which of the following statements is true?

Accepted Answer

The smallest value $$f(x)$$ can take is 0.

Question 7

Which of the following points is a y-intercept of the function whose graph passes through $$(0, -6)$$?

Accepted Answer

$$(0, -6)$$

Question 8

On which interval is the function in the image increasing?

Accepted Answer

$$(-\infty, -1)$$ and $$(1, \infty)$$

Question 9

A function $$f is $$even if:

Accepted Answer

$$f(-x) = f(x)$$ for all $$x in $$the domain of $$f$$

Question 10

Given the piecewise function $$C(x) = \begin{cases} 20 & 	ext{if } x \leq 60 \ 20 + 0.40(x-60) & 	ext{if } x \u003e 60 \end{cases}$$, what is $$C(80)$$?

Accepted Answer

$$28$$

Question 11

What is the difference quotient for $$f(x) = -2x^2$ + x + 5$$?

Accepted Answer

$$-4x - 2h + 1$$

Question 12

Find the slope of the line passing through the points $$(4, -2)$$ and $$(-1, 5).$$

Accepted Answer

$$-\dfrac{7}{5}$$

Question 13

Which of the following is the equation of a horizontal line passing through $$(0, 3)$$?

Accepted Answer

$$y = 3$$

Question 14

Given the equation $$3x + 6y - 12 = 0$$, what is the slope and y-intercept?

Accepted Answer

Slope: $$-\dfrac{1}{2}$$, y-intercept: $$2$$

Question 15

If two nonvertical lines are parallel, what can be said about their slopes?

Accepted Answer

Their slopes are equal.

Question 16

A line has equation $$y = 3x + 1. $$What is the equation of the line passing through $$(-2, 5)$$ and parallel to this line?

Accepted Answer

$$y - 5 = 3(x + 2)$$

Question 17

If a line has slope $$m$$, what is the slope of a line perpendicular to it?

Accepted Answer

$$-\dfrac{1}{m}$$

Question 18

In a real-world context, the slope of a linear function modeling the number of adult men living alone in the U.S. from 1990 to 2008 is $$0.32. $$What does this number represent?

Accepted Answer

The rate of increase in millions of men per year.

Question 19

Given $$f(x) = x^3$, what is the average rate of change from x = -2$ to x = 0$?

Accepted Answer

$$4$$

Functions and Graphs: Foundations for Algebra and Trigonometry

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