Absolute Value Parent Functions Solutions

Non-Polynomial Parent Functions
Type	Absolute Value	Square Root	Cube Root	Reciprocal
Parent equation	$y=\left|x\right|$
Degree	does not apply
Domain and Range	$$\begin{gathered} \mathrm{domain}:\left\{x|x\in \mathrm{ℝ}\right\} \\ \mathrm{range}:\left\{y|y\in \mathrm{ℝ}, y\ge 0\right\} \end{gathered}$$
Quadrants	Q1 and Q2
Because	y-coordinates will always be positive because $\left|\mathrm{term}\right|=+\mathrm{term}$
Other Characteristics	v-shaped, symmetric Axis of symmetry is $x=0,$ the y-axis
Intersects graph	vertex at origin, changes directions at origin

Example 6

Graph the absolute value parent function. Name the domain and range in interval and set-builder notation. Then name the end behavior of the graph.

End behavior

As $x\to +\infty , f\left(x\right)\to \underline{ +\infty },$ and as $x\to –\infty , \underline{ f\left(x\right)\to +\infty }$