Beginning and Intermediate Algebra

Margaret L. Lial, John Hornsby, Terry McGinnis

Chapter 13

Nonlinear Functions, Conic Sections, and Nonlinear Systems - all with Video Answers

Educators

Section 1

Additional Graphs of Functions

Problem 1

Refer to the basic graphs in $A-F$ to answer each of the following.
Which is the graph of $f(x)=|x|$ ? The lowest point on its graph has coordinates (_____,_____)

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Problem 2

Refer to the basic graphs in A–F to answer each of the following.
Which is the graph of $f(x)=x^{2}$ ? Give the domain and range.

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Problem 3

Refer to the basic graphs in A–F to answer each of the following.
Which is the graph of $f(x)=[x] ?$ Give the domain and range.

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Problem 4

Refer to the basic graphs in A–F to answer each of the following
Which is the graph of $f(x)=\sqrt{x} ?$ Give the domain and range.

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Problem 5

Refer to the basic graphs in A–F to answer each of the following.
Which is not the graph of a function? Why?

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Problem 6

Refer to the basic graphs in A–F to answer each of the following
Which is the graph of $f(x)=\frac{1}{x} ?$ The lines with equations $x=0$ and $y=0$ are called its __________.

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Problem 7

Without actually plotting points, match cach function defined by the absolute value expression with its graph.
$$
f(x)=|x-2|+2
$$

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Problem 8

Without actually plotting points, match each function defined by the absolute
value expression with its graph.
$$
f(x)=|x+2|+2
$$

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Problem 9

Without actually plotting points, match each function defined by the absolute
value expression with its graph
$$
f(x)=|x-2|-2
$$

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Problem 10

Without actually plotting points, match each function defined by the absolute
value expression with its graph.
$$
f(x)=|x+2|-2
$$

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Problem 11

How is the graph of $f(x)=\frac{1}{x-3}+2$ obtained from the graph of $g(x)=\frac{1}{x} ?$

James Kiss

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Problem 12

How is the graph of $f(x)=\frac{1}{x+5}-3$ obtained from the graph of $g(x)=\frac{1}{x} ?$

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Problem 13

Graph each function. Give the domain and range.
$f(x)=|x+1|$

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Problem 14

Graph each function. Give the domain and range.
$f(x)=|x-1|$

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Problem 15

Graph each function. Give the domain and range.
$f(x)=\frac{1}{x}+1$

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Problem 16

Graph each function. Give the domain and range.
$f(x)=\frac{1}{x}-1$

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Problem 17

Graph each function. Give the domain and range.
$f(x)=\sqrt{x-2}$

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Problem 18

Graph each function. Give the domain and range.
$f(x)=\sqrt{x+5}$

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Problem 19

Graph each function. Give the domain and range.
$f(x)=\frac{1}{x-2}$

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Problem 20

Graph each function. Give the domain and range.
$f(x)=\frac{1}{x+2}$

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Problem 21

Graph each function. Give the domain and range.
$f(x)=\sqrt{x+3}-3$

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Problem 22

Graph each function. Give the domain and range.
$f(x)=\sqrt{x-2}+2$

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Problem 23

Graph each function. Give the domain and range.
$f(x)=|x-3|+1$

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Problem 24

Graph each function. Give the domain and range.
$f(x)=|x+1|-4$

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Problem 25

A student incorrectly evaluated [-5.1] as $-5 .$ Evaluate correctly.

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Problem 26

A student incorrectly evaluated [3.75] as 4. Evaluate correctly.

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Problem 27

Evaulate each expression. See Example $4 .$
[3]

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Problem 28

Evaulate each expression.
$[18]$

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Problem 29

Evaluate each expression.
[4.5]

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Problem 30

Evaluate each expression.
$[8.7]$

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Problem 31

Evaluate each expression.
$\left[\frac{1}{2}\right]$

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Problem 32

Evaluate each expression.
$\left[\frac{3}{4}\right]$

AG

Ankit Gupta

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Problem 33

Evaluate each expression.
$\left[\frac{8}{3}\right]$

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Problem 34

Evaluate each expression.
$\left[\frac{5}{2}\right]$

Elizabeth Xu

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Problem 35

Evaluate each expression.
[-14]

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Problem 36

Evaluate each expression.
[-5]

Michael Lubich

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Problem 37

Evaluate each expression.
[-10.1]

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Problem 38

Evaluate each expression.
[-6.9]

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Problem 39

Graph each step function.
$f(x)=[x-3]$

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Problem 40

Graph each step function.
$f(x)=[x+2]$

Heather Zimmers

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Problem 41

Graph each step function.
$f(x)=[x]-1$

Heather Zimmers

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Problem 42

Graph each step function.
$f(x)=[x]+1$

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Problem 43

Solve each problem.
Suppose that postage rates are $\$ 0.55$ for the first ounce, plus $\$ 0.24$ for each additional ounce, and that each letter carries one $\$ 0.55$ stamp and as many $\$ 0.24$ stamps as necessary. Graph the function
$y=p(x)=$ the number of stamps
on a letter weighing $x$ ounces. Use the interval (0,5]

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Problem 44

The cost of parking a car at an airport hourly parking lot is $\$ 3$ for the first half-hour and $\$ 2$ for each additional half-hour or fraction thereof. Graph the function
$y=f(x)=$ the cost of parking a car
for $x$ hours. Use the interval $(0,2] .$

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Problem 45

A certain long-distance carrier provides service between Podunk and Nowhereville. If $x$ represents the number of minutes for the call, where $x>0,$ then the function $f$ defined by
$$
f(x)=0.40[x]+0.75
$$

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Problem 46

Total rental cost in dollars for a power washer, where $x$ represents the number of hours with $x>0,$ can be represented by the function
$$
f(x)=12[x]+25
$$
Find the cost of a $7 \frac{1}{2}$ -hr rental.

Willis James

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