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 equation $$y^2 = 1$$ - $$x^2$$, does this equation define $$y as a $$function of $$x$$?

Accepted Answer

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

Question 3

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

Accepted Answer

A graph is a function if every vertical line intersects it at most once.

Question 4

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

Accepted Answer

$$-1$$

Question 5

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 function is only defined for $$x$$ between $$-2$$ and $$1$$, inclusive.

Question 6

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

Accepted Answer

$$(0, -6)$$

Question 7

A function $$f is $$increasing on $$(-\infty, -1)$$, decreasing on $$(-1, 1)$$, and increasing on $$(1, \infty). $$What can you conclude about $$f at$$ $$x = -1$$ and $$x = 1$$?

Accepted Answer

$$f$$ has a relative maximum at $$x = -1$$ and a relative minimum at $$x = 1.$$

Question 8

Which of the following is true for an even function $$f$$?

Accepted Answer

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

Question 9

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 10

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

Accepted Answer

$$2x + h$$

Question 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

$$y = 3$$

Question 13

Given the general form $$3x + 6y - 12 = 0$$, what is the slope and y-intercept of the line?

Accepted Answer

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

Question 14

A line passes through $$(2, -5)$$ and has a slope of $$6. $$What is its equation in slope-intercept form?

Accepted Answer

$$y = 6x - 17$$

Question 15

If two nonvertical lines are perpendicular and one has slope $$m$$, what is the slope of the other?

Accepted Answer

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

Question 16

A real-world application: In 1990, 9 million adult men in the US lived alone. In 2008, 14.7 million did. What is the average rate of change in millions per year?

Accepted Answer

$$0.32$$

Question 17

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

Accepted Answer

$$4$$

Question 18

Which of the following statements about the graph of a function is correct?

Accepted Answer

A function can have more than one x-intercept.

Question 19

If a function $$f is $$defined as $$f(x) = x^5$ + 1$$, is it even, odd, or neither?

Accepted Answer

Neither

Functions and Graphs: Foundations, Properties, and Linear Models

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