Question

Sketch the graph of the piece wise defined function $f\left(x\right)=\left\{\begin{array}{l}2x+3ifx<-1\\ 3-xifx\ge -1\end{array}\right\}$.

Short answer

The graph of the piece wise defined function $f\left(x\right)=\left\{\begin{array}{l}2x+3ifx<-1\\ 3-xifx\ge -1\end{array}\right\}$is shown.

Step-by-step solution

Step 1. Construct the table for the given function.

The given function is $f\left(x\right)=\left\{\begin{array}{l}2x+3ifx<-1\\ 3-xifx\ge -1\end{array}\right\}$whose tables for respective values of$\left(x\right)$and$f\left(x\right)$ is shown below.

$x$	-1	2	1	0
$f\left(x\right)$	1	1	2	3

Step 2. Plot the points on coordinate plane.

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

Step 3. DESCRIPTION OF STEPS.

The obtained graph is a piece wise graph of the function $f\left(x\right)=\left\{\begin{array}{l}2x+3ifx<-1\\ 3-xifx\ge -1\end{array}\right\}$.