Question

Sketch the graph of the piece wise defined function $f\left(x\right)=\left\{\begin{array}{l}{x}^2\text{if}\left|x\right|\le 1\\ 1\text{if}\left|x\right|>1\end{array}\right\}$.

Short answer

The graph of the piece wise defined function $f\left(x\right)=\left\{\begin{array}{l}{x}^2\text{if}\left|x\right|\le 1\\ 1\text{if}\left|x\right|>1\end{array}\right\}$is shown.

Step-by-step solution

Step 1. Construct the table for the given function.

The given function is $f\left(x\right)=\left\{\begin{array}{l}{x}^2\text{if}\left|x\right|\le 1\\ 1\text{if}\left|x\right|>1\end{array}\right\}$whose tables for respective values of $\left(x\right)$and $f\left(x\right)$is shown below.

$x$	0	1	-1	2	4
$f\left(x\right)$	0	1	1	1	1

Step 2. Plot the points on coordinate plane.

By plotting points on coordinate plane, the graph for the piece wise function $f\left(x\right)=\left\{\begin{array}{l}{x}^2\text{if}\left|x\right|\le 1\\ 1\text{if}\left|x\right|>1\end{array}\right\}$is shown below.

Step 3. DESCRIPTION OF STEPS.

The obtained graph is a piece wise graph of the function $f\left(x\right)=\left\{\begin{array}{l}{x}^2\text{if}\left|x\right|\le 1\\ 1\text{if}\left|x\right|>1\end{array}\right\}$.