CPM Homework Help : PC3 Problem 1-137

Sketch the graph of the piecewise-defined function below and determine if the graph is continuous.

$f ( x ) = \left\{ \begin{array} { c c c } { - x + 5 } & { \text { for } } & { x < - 2 } \\ { ( x - 1 ) ^ { 2 } - 2 } & { \text { for } } & { - 2 \leq x < 3 } \\ { - x + 5 } & { \text { for } } & { x \geq 3 } \end{array} \right.$

Step:

For $x<-2$

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

For $-2 \leq x <3$

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

For $x \geq 3$

$x$	$f\left(x\right)=-x+5$
$3$
$4$
$5$
$6$