Square Root Parent Functions Solutions

Non-Polynomial Parent Functions
Type	Absolute Value	Square Root	Cube Root	Reciprocal
Parent equation	$y=\left|x\right|$	$y=\sqrt{x}$
Degree	does not apply	$\frac{1}{2}$
Domain and Range	$$\begin{gathered} \mathrm{domain}:\left\{x|x\in \mathrm{ℝ}\right\} \\ \mathrm{range}:\left\{y|y\in \mathrm{ℝ}, y\ge 0\right\} \end{gathered}$$	$$\begin{gathered} \mathrm{domain}:\left\{x|x\in \mathrm{ℝ}, x\ge 0\right\} \\ \mathrm{range}:\left\{y|y\in \mathrm{ℝ}, y\ge 0\right\} \end{gathered}$$
Quadrants	Q1 and Q2	Q1
Because	y-coordinates will always be positive because $\left|\mathrm{term}\right|=+\mathrm{term}$	only $\mathrm{ℝ}$ are being graphed, so the x- and y-values will be ≥ zero
Other Characteristics	v-shaped, symmetric Axis of symmetry is $x=0,$ the y-axis	partial inverse of the quadratic function
Intersects graph	vertex at origin, changes directions at origin	defined start and end point at the origin

Example 7

Graph the square root 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 $x\to 0, \underline{ f\left(x\right)\to 0 }$

Note

When graphing the square root function, it is helpful to pick values for x that will result in the square root of a perfect square so that the ordered pairs can be graphed accurately.