Cubic Parent Functions Solutions

Polynomial Parent Functions
Type	Linear	Quadratic	Cubic
Parent equation	y = x	$y=x^2$	$y=x^3$
Degree	1	2	3
Domain and Range	$$\begin{gathered} \mathrm{domain}:\left\{x|x\in \mathrm{ℝ}\right\} \\ \mathrm{range}:\left\{y|y\in \mathrm{ℝ}\right\} \end{gathered}$$	$$\begin{gathered} \mathrm{domain}:\left\{x|x\in \mathrm{ℝ}\right\} \\ \mathrm{range}:\left\{y|y\in \mathrm{ℝ}, y\ge 0\right\} \end{gathered}$$	$$\begin{gathered} \mathrm{domain}:\left\{x|x\in \mathrm{ℝ}\right\} \\ \mathrm{range}:\left\{y|y\in \mathrm{ℝ}\right\} \end{gathered}$$
Quadrants	Q1 and Q3	Q1 and Q2	Q1 and Q3
Because	the x- and y-coordinates will always have the same value	the y-coordinates will always be positive, because any number squared is positive	when the x-value is positive, the y-value is positive, and when the x-value is negative, the y-value is negative
Other Characteristics	slope $m=1$	parabola, u-shaped symmetric graph Axis of symmetry is $x=0$, the y-axis
Intersects graph	Polynomial parent functions intersect the coordinate plane at the origin: (0, 0)

Example 5

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

End behavior

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