Section 1
Functions
Determine whether each relation is a function. Explain.$$\{(13,5),(-4,12),(6,0),(13,10)\}$$
Determine whether each relation is a function. Explain.$$\{(9.2,7),(9.4,11),(9.5,9.5),(9.8,8)\}$$
Determine whether each relation is a function. Explain.$$\begin{array}{|c|c|}\hline \text { Domain } & \text { Range } \\\hline-3 & 3 \\\hline-1 & -2 \\\hline 0 & 5 \\\hline 1 & -4 \\\hline 2 & 3 \\\hline\end{array}$$
Determine whether each relation is a function. Explain.$$\begin{array}{|r|r|}\hline x & y \\\hline 5 & 4 \\\hline 2 & 8 \\\hline-7 & 9 \\\hline 2 & 12 \\\hline 5 & 14 \\\hline\end{array}$$
Determine whether each relation is a function. Explain.(GRAPH CANT COPY)
Use the data in the table.(GRAPH CANT COPY)Do the data represent a function? Explain.
Use the data in the table.(GRAPH CANT COPY)Is there any relation between foot length and height?
Determine whether each relation is a function. Explain.$$\{(-1,6),(4,2),(2,36),(1,6)\}$$
Determine whether each relation is a function. Explain.$$\{(-2,3),(4,7),(24,-6),(5,4)\}$$
Determine whether each relation is a function. Explain.$$\{(9,18),(0,36),(6,21),(6,22)\}$$
Determine whether each relation is a function. Explain.$$\{(5,-4),(-2,3),(5,-1),(2,3)\}$$
Determine whether each relation is a function. Explain.$$\begin{array}{|c|c|}\hline \text { Domain } & \text { Range } \\\hline-4 & -2 \\\hline-2 & 1 \\\hline 0 & 2 \\\hline 3 & 1 \\\hline\end{array}$$
Determine whether each relation is a function. Explain.$$\begin{array}{|c|c|}\hline \text { Domain} & \text { Range } \\\hline-1 & 5 \\\hline-2 & 5 \\\hline-2 & 1 \\\hline-6 & 1 \\\hline\end{array}$$
Determine whether each relation is a function. Explain.$$\begin{array}{|r|r|}\hline x & y \\\hline-7 & 2 \\\hline 0 & 4 \\\hline 11 & 6 \\\hline 11 & 8 \\\hline 0 & 10 \\\hline\end{array}$$
Determine whether each relation is a function. Explain.$$\begin{array}{|r|r|}\hline x & y \\\hline 14 & 5 \\\hline 15 & 10 \\\hline 16 & 15 \\\hline 17 & 20 \\\hline 18 & 25 \\\hline\end{array}$$
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.
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.
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.
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.
Tell whether each statement is always, sometimes, or never true. Explain.A function is a relation.
Tell whether each statement is always, sometimes, or never true. Explain.A relation is a function.
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.
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.
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.
Draw the graph of a relation that is not a function. Explain why it is not a function.
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.
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.
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.
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.
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.$$\begin{array}{|c|c|}\hline x & y \\\hline-4 & -4 \\\hline 2 & 16 \\\hline 5 & 8 \\\hline 10 & -4 \\\hline 12 & 15 \\\hline\end{array}$$
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.
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.
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 $\$ 49$
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
The length of a DNA strand is 0.0000007 meter. Write the length of a DNA strand using scientific notation.
Evaluate each expression if $x=4$ and $y=-1.$$$3 x+1$$
Evaluate each expression if $x=4$ and $y=-1.$$$2 y$$
Evaluate each expression if $x=4$ and $y=-1.$$$y+6$$
Evaluate each expression if $x=4$ and $y=-1.$$$20-4 x$$