Question

Sketch the graph of the piece wise defined function $f\left(x\right)=\left\{\begin{array}{l}4\text{if}x<-2\\ x^2\text{if}-2\le x\le 2\\ -x+6\text{if}x>2\end{array}\right\}$.

Short answer

The graph of the piece wise defined function $f\left(x\right)=\left\{\begin{array}{l}4\text{if}x<-2\\ x^2\text{if}-2\le x\le 2\\ -x+6\text{if}x>2\end{array}\right\}$is shown.

Step-by-step solution

Step 1. Construct the table for the given function.

The given function is$f\left(x\right)=\left\{\begin{array}{l}4\text{if}x<-2\\ x^2\text{if}-2\le x\le 2\\ -x+6\text{if}x>2\end{array}\right\}$whose tables for respective values of$\left(x\right)$and$f\left(x\right)$

$x$	-5	-3	-2	2	3	4
$f\left(x\right)$	4	4	4	4	3	2

is shown below.

Step 2. Plot the points on coordinate plane.

By plotting points on coordinate plane, the graph for the piece wise function $f\left(x\right)=\left\{\begin{array}{l}4\text{if}x<-2\\ x^2\text{if}-2\le x\le 2\\ -x+6\text{if}x>2\end{array}\right\}$is shown below.

Step 3. Description of steps.

The obtained graph is a piece wise graph of the function $f\left(x\right)=\left\{\begin{array}{l}4\text{if}x<-2\\ x^2\text{if}-2\le x\le 2\\ -x+6\text{if}x>2\end{array}\right\}$.