Beginning and Intermediate Algebra

Margaret L. Lial , John Hornsby

Chapter 13

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

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Section 1

Additional Graphs of Functions

Problem 1

Refer to the basic graphs in $A-F$. (GRAPH CANNOT COPY).
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 $A-F$. (GRAPH CANNOT COPY).
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 $A-F$. (GRAPH CANNOT COPY).
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 $A-F$. (GRAPH CANNOT COPY).
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 $A-F$. (GRAPH CANNOT COPY).
Which is not the graph of a function? Why?

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Problem 6

Refer to the basic graphs in $A-F$. (GRAPH CANNOT COPY).
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 each function defined by the absolute value expression with its graph. (GRAPH CANNOT COPY).
$$
f(x)=|x-2|+2
$$

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Problem 8

Without actually plotting points, match each function defined by the absolute value expression with its graph. (GRAPH CANNOT COPY).
$$
f(x)=|x+2|+2
$$

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Problem 9

Without actually plotting points, match each function defined by the absolute value expression with its graph. (GRAPH CANNOT COPY).
$$
f(x)=|x-2|-2
$$

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Problem 10

Without actually plotting points, match each function defined by the absolute value expression with its graph. (GRAPH CANNOT COPY).
$$
f(x)=|x+2|-2
$$

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Problem 11

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

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Problem 12

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

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Problem 13

Graph each function. Give the domain and range. See Examples $1-3$.
$$
f(x)=\frac{1}{x}+1
$$

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Problem 14

Graph each function. Give the domain and range. See Examples $1-3$.
$$
f(x)=\frac{1}{x}-1
$$

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Problem 15

Graph each function. Give the domain and range. See Examples $1-3$.
$$
f(x)=\sqrt{x-2}
$$

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Problem 16

Graph each function. Give the domain and range. See Examples $1-3$.
$$
f(x)=\sqrt{x+5}
$$

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Problem 17

Graph each function. Give the domain and range. See Examples $1-3$.
$$
f(x)=\frac{1}{x-2}
$$

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Problem 18

Graph each function. Give the domain and range. See Examples $1-3$.
$$
f(x)=\frac{1}{x+2}
$$

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Problem 19

Graph each function. Give the domain and range. See Examples $1-3$.
$$
f(x)=\sqrt{x+3}-3
$$

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Problem 20

Graph each function. Give the domain and range. See Examples $1-3$.
$$
f(x)=\sqrt{x-2}+2
$$

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Problem 21

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

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Problem 22

Graph each function. Give the domain and range. See Examples $1-3$.
$$
f(x)=|x+1|-4
$$

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Problem 23

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

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Problem 24

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 25

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

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Problem 26

Evaluate each expression. See Example 4.
$$
[[18]]
$$

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Problem 27

Evaluate each expression. See Example 4.
$$
[[4.5]]
$$

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Problem 28

Evaluate each expression. See Example 4.
$$
[[8.7]]
$$

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Problem 29

Evaluate each expression. See Example 4.
$$
[[\frac{1}{2}]]
$$

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Problem 30

Evaluate each expression. See Example 4.
$$
[[\frac{3}{4}]]
$$

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Problem 31

Evaluate each expression. See Example 4.
$$
[[-14]]
$$

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Problem 32

Evaluate each expression. See Example 4.
$$
[[-5]]
$$

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Problem 33

Evaluate each expression. See Example 4.
$$
[[-10.1]]
$$

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Problem 34

Evaluate each expression. See Example 4.
$$
[[-6.9]]
$$

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Problem 35

Graph each step function. See Examples 5 and 6.
$$
f(x)= [[x]] -1
$$

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Problem 36

Graph each step function. See Examples 5 and 6.
$$
f(x)= [[ x ]]+1
$$

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Problem 37

Graph each step function. See Examples 5 and 6.
$$
f(x)=[[ x-3 ]]
$$

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Problem 38

Graph each step function. See Examples 5 and 6.
$$
f(x)=[[ x+2 ]]
$$

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Problem 39

Assume that postage rates are $44 é$ for the first ounce, plus $17 \notin$ for each additional ounce, and that each letter carries one $44 \notin$ stamp and as many $17 \notin$ stamps as necessary. Graph the function defined by $y=p(x)=$ the number of stamps on a letter weighing $x$ ounces. Use the interval $(0,5]$.

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Problem 40

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

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Problem 41

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
$$
f(x)=0.40 [[ x ]]+0.75
$$
gives the total cost of the call in dollars. Find the cost of a 5.5 -minute call.

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Problem 42

See Exercise $41 .$ Find the cost of a 20.75 -minute call.

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Problem 43

Find the distance between each pair of points. See Section 10.3 .
$$
(2,-1) \text { and }(4,3)
$$

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Problem 44

Find the distance between each pair of points. See Section 10.3 .
$$
(x, y) \text { and }(-2,5)
$$

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Problem 45

Find the distance between each pair of points. See Section 10.3 .
$$
(x, y) \text { and }(h, k)
$$

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