Explore: Linear Parent Functions Solutions

Polynomial Parent Functions
Type	Linear	Quadratic	Cubic
Parent equation	y = x
Degree	1
Domain and Range	$$\begin{gathered} \mathrm{domain}:\left\{x|x\in \mathrm{ℝ}\right\} \\ \mathrm{range}:\left\{y|y\in \mathrm{ℝ}\right\} \end{gathered}$$
Quadrants	Q1 and Q3
Because	the x- and y-coordinates will always have the same value
Other Characteristics	slope $m=1$
Intersects graph	Polynomial parent functions intersect the coordinate plane at the origin: (0, 0)

Example 3

Graph the linear 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 $x\to –\infty , \underline{ f\left(x\right)\to –\infty }$

Note

The linear parent function and the many forms of linear functions are covered fully in Algebra 1: Principles of Secondary Mathematics.