91Ó°ÊÓ

Verifying Points of Intersection How can you check that an ordered pair is a point of intersection of two graphs?

Transformations What are the three basic types of function transformations?

Right and Left Behavior Describe the four cases of the Leading Coefficient Test.

Finding the Domain and Range of a Piecewise Function In Exercises \(27-30\) , evaluate the function at the given value(s) of the independent variable. Then find the domain and range. \(f(x)=\left\\{\begin{array}{ll}{2 x+1,} & {x<0} \\\ {2 x+2,} & {x \geq 0}\end{array}\right.\) $$$$ \(\begin{array}{llll}{\text { (a) } f(-1)} & {\text { (b) } f(0)} & {\text { (c) } f(2)} & {\text { (d) } f\left(t^{2}+1\right)}\end{array}\)

Modeling Data The table shows the populations \(y\) (in millions) of the United States for 2009 through \(2014 .\) The variable \(t\) represents the time in years, with \(t=9\) corresponding to \(2009 . \quad\) (Source: \(U . S .\) Census Bureau) $$\begin{array}{|c|c|c|c|c|c|c|}\hline t & {9} & {10} & {11} & {12} & {13} & {14} \\ \hline y & {307.0} & {309.3} & {311.7} & {314.1} & {316.5} & {318.9} \\\ \hline\end{array}$$ (a) Plot the data by hand and connect adjacent points with a line segment. Use the slope of each line segment to determine the year when the population increased least rapidly. (b) Find the average rate of change of the population of the United States from 2009 through \(2014 .\) (c) Use the average rate of change of the population to predict the population of the United States in \(2025 .\)

Sketching a Graph of a Function In Exercises \(31-38,\) sketch a graph of the function and find its domain and range. Use a graphing utility to verify your graph. \(f(x)=\sqrt{9-x^{2}}\)

Testing for Symmetry In Exercises \(29-40\) , test for symmetry with respect to each axis and to the origin. \(|y|-x=3\)

Deciding Whether an Equation Is a Function In Exercises \(43-46,\) determine whether \(y\) is a function of \(x\). $$y^{2}=x^{2}-1$$

Using Intercepts and Symmetry to Sketch a Graph In Exercises \(41-56,\) find any intercepts and test for symmetry. Then sketch the graph of the equation. \(x=y^{4}-16\)

Using Intercepts and Symmetry to Sketch a Graph In Exercises \(41-56,\) find any intercepts and test for symmetry. Then sketch the graph of the equation. \(y=6-|x|\)