🎉 Announcing Numerade's $26M Series A, led by IDG Capital!Read how Numerade will revolutionize STEM Learning

Prealgebra

Carol E. Malloy, Rhonda J. Molix-Bailey, Jack Price

Chapter 7

Functions and Graphing

Educators


Problem 1

Determine whether each relation is a function. Explain.
$$\{(13,5),(-4,12),(6,0),(13,10)\}$$

Brandon F.
Numerade Educator

Problem 2

Determine whether each relation is a function. Explain.
$$\{(9.2,7),(9.4,11),(9.5,9.5),(9.8,8)\}$$

Brandon F.
Numerade Educator

Problem 3

Determine whether each relation is a function. Explain.
$$\begin{array}{|c|c|}\hline \text { Domain } & \text { Range } \\\hline-3 & 3 \\\hline-1 & -2 \\\hline 0 & 5 \\\hline 1 & -4 \\
\hline 2 & 3 \\\hline\end{array}$$

Brandon F.
Numerade Educator

Problem 4

Determine whether each relation is a function. Explain.
$$\begin{array}{|r|r|}\hline x & y \\\hline 5 & 4 \\\hline 2 & 8 \\\hline-7 & 9 \\\hline 2 & 12 \\\hline 5 & 14 \\\hline
\end{array}$$

Brandon F.
Numerade Educator

Problem 5

Determine whether each relation is a function. Explain.
(GRAPH CANT COPY)

Brandon F.
Numerade Educator

Problem 6

Determine whether each relation is a function. Explain.
(GRAPH CANT COPY)

Brandon F.
Numerade Educator

Problem 7

Use the data in the table.
(GRAPH CANT COPY)
Do the data represent a function? Explain.

Brandon F.
Numerade Educator

Problem 8

Use the data in the table.
(GRAPH CANT COPY)
Is there any relation between foot length and height?

Brandon F.
Numerade Educator

Problem 9

Determine whether each relation is a function. Explain.
$$\{(-1,6),(4,2),(2,36),(1,6)\}$$

Brandon F.
Numerade Educator

Problem 10

Determine whether each relation is a function. Explain.
$$\{(-2,3),(4,7),(24,-6),(5,4)\}$$

Brandon F.
Numerade Educator

Problem 11

Determine whether each relation is a function. Explain.
$$\{(9,18),(0,36),(6,21),(6,22)\}$$

Brandon F.
Numerade Educator

Problem 12

Determine whether each relation is a function. Explain.
$$\{(5,-4),(-2,3),(5,-1),(2,3)\}$$

Brandon F.
Numerade Educator

Problem 13

Determine whether each relation is a function. Explain.
$$\begin{array}{|c|c|}\hline \text { Domain } & \text { Range } \\\hline-4 & -2 \\\hline-2 & 1 \\
\hline 0 & 2 \\\hline 3 & 1 \\\hline\end{array}$$

Brandon F.
Numerade Educator

Problem 14

Determine whether each relation is a function. Explain.
$$\begin{array}{|c|c|}\hline \text { Domain} & \text { Range } \\\hline-1 & 5 \\\hline-2 & 5 \\\hline-2 & 1 \\
\hline-6 & 1 \\\hline\end{array}$$

Brandon F.
Numerade Educator

Problem 15

Determine whether each relation is a function. Explain.
$$\begin{array}{|r|r|}\hline x & y \\\hline-7 & 2 \\\hline 0 & 4 \\\hline 11 & 6 \\\hline 11 & 8 \\\hline 0 & 10 \\
\hline\end{array}$$

Brandon F.
Numerade Educator

Problem 16

Determine whether each relation is a function. Explain.
$$\begin{array}{|r|r|}\hline x & y \\\hline 14 & 5 \\\hline 15 & 10 \\\hline 16 & 15 \\\hline 17 & 20 \\\hline 18 & 25 \\
\hline\end{array}$$

Brandon F.
Numerade Educator

Problem 17

Determine whether each relation is a function. Explain.
(GRAPH CANT COPY)

Brandon F.
Numerade Educator

Problem 18

Determine whether each relation is a function. Explain.
(GRAPH CANT COPY)

Brandon F.
Numerade Educator

Problem 19

Determine whether each relation is a function. Explain.
(GRAPH CANT COPY)

Brandon F.
Numerade Educator

Problem 20

Determine whether each relation is a function. Explain.
(GRAPH CANT COPY)

Brandon F.
Numerade Educator

Problem 21

Use the table that shows the number and size of farms in the United States every decade from 1950 to 2000.
(TABLE CANT COPY)
Is the relation (year, number of farms) a function? Explain.

Brandon F.
Numerade Educator

Problem 22

Use the table that shows the number and size of farms in the United States every decade from 1950 to 2000.
(TABLE CANT COPY)
Describe how the number of farms is related to the year.

Brandon F.
Numerade Educator

Problem 23

Use the table that shows the number and size of farms in the United States every decade from 1950 to 2000.
(TABLE CANT COPY)
Is the relation (number of farms, average size of farms) a function? Explain.

Brandon F.
Numerade Educator

Problem 24

Is the relation (number of farms, average size of farms) a function? Explain.
Describe how the average size of farms is related to the year.

Brandon F.
Numerade Educator

Problem 25

Tell whether each statement is always, sometimes, or never true. Explain.
A function is a relation.

Brandon F.
Numerade Educator

Problem 26

Tell whether each statement is always, sometimes, or never true. Explain.
A relation is a function.

Brandon F.
Numerade Educator

Problem 27

Use the table that shows how various wind speeds affect the actual temperature of $15^{\circ} \mathrm{F}.$
(TABLE CANT COPY)
Do the data represent a function? Explain.

Brandon F.
Numerade Educator

Problem 28

Use the table that shows how various wind speeds affect the actual temperature of $15^{\circ} \mathrm{F}.$
(TABLE CANT COPY)
Describe how wind chill temperatures are related to wind speed.

Brandon F.
Numerade Educator

Problem 29

RESEARCH Use the Internet or another source to find the complete wind chill table. Does the data for actual temperature and wind chill temperature for a specific wind speed represent a function? Explain.

Check back soon!

Problem 30

Draw the graph of a relation that is not a function. Explain why it is not a function.

Brandon F.
Numerade Educator

Problem 31

Describe three ways to represent a function. Show an example of each. Then describe three ways to represent a relation that is not a function and show an example of each.

Check back soon!

Problem 32

The inverse of any relation is obtained by switching the coordinates in each ordered pair of the relation.
Determine whether the inverse of the relation $\{(4,0),(5,1),(6,2),(6,3)\}$ is a function.

Check back soon!

Problem 33

The inverse of any relation is obtained by switching the coordinates in each ordered pair of the relation.
Is the inverse of a function always, sometimes, or never a function? Give an example to explain your reasoning.

Check back soon!

Problem 34

The inverse of any relation is obtained by switching the coordinates in each ordered pair of the relation.
How can the relationship between water depth and time to ascend to the water's surface be a function? Include a discussion about whether water depth can ever have two corresponding times to ascend to the water's surface.

Check back soon!

Problem 35

Which statement is true about the data in the table?
A The data represent a function.
B The data do not represent a function.
C As the value of $x$ increases, the value of $y$ increases.
D A graph of the data would not pass the vertical line test.
$$\begin{array}{|c|c|}\hline x & y \\\hline-4 & -4 \\\hline 2 & 16 \\\hline 5 & 8 \\\hline 10 & -4 \\\hline 12 & 15 \\
\hline\end{array}$$

Brandon F.
Numerade Educator

Problem 36

F The water temperature stays the same as the depth increases.
G The water temperature decreases as the depth increases.
H The water temperature increases as the depth increases.
J The water temperature decreases as the depth decreases.

Brandon F.
Numerade Educator

Problem 37

TECHNOLOGY The table shows the results of a survey in which middle school students were asked whether they ever used the Internet for the activities listed. Use the data to predict how many students in a middle school of 650 have used the Internet to do research for school.

Check back soon!

Problem 38

Find each percent of change. Round to the nearest tenth, if necessary. Then state whether the percent of change is a percent of increase or a percent of decrease.
from $\$ 56$ to $\$ 49$

Brandon F.
Numerade Educator

Problem 39

Find each percent of change. Round to the nearest tenth, if necessary. Then state whether the percent of change is a percent of increase or a percent of decrease.
from 110 mg to 165 mg

Brandon F.
Numerade Educator

Problem 40

The length of a DNA strand is 0.0000007 meter. Write the length of a DNA strand using scientific notation.

Brandon F.
Numerade Educator

Problem 41

Evaluate each expression if $x=4$ and $y=-1.$
$$3 x+1$$

Brandon F.
Numerade Educator

Problem 42

Evaluate each expression if $x=4$ and $y=-1.$
$$2 y$$

Brandon F.
Numerade Educator

Problem 43

Evaluate each expression if $x=4$ and $y=-1.$
$$y+6$$

Brandon F.
Numerade Educator

Problem 44

Evaluate each expression if $x=4$ and $y=-1.$
$$20-4 x$$

Brandon F.
Numerade Educator