Question

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

Short answer

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

Step-by-step solution

Step 1. Construct the table for the given function.

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

$x$	-2	-3	-1	1	2	3
$f\left(x\right)$	-1	-1	1	1	-1	-1

Step 2. Plot the points on coordinate plane.

By plotting points $\left(-2,-1\right),\left(-3,-1\right),\left(-1,1\right),\left(1,1\right),\left(2,-1\right),\left(3,-1\right)$on coordinate plane, the graph for the piece wise function $f\left(x\right)=\left\{\begin{array}{l}-1\text{if}x<-1\\ 1\text{if}-1\le x\le 1\\ -1\text{if}x>1\end{array}\right\}$is shown below.

Step 3. DESCRIPTION OF STEPS.

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