### Home > PC3 > Chapter 1 > Lesson 1.3.3 > Problem1-137

1-137.

Sketch the graph of the piecewise-defined function below and determine if the graph is continuous.
$f ( x ) = \left\{ \begin{array} { c c c } { - x + 5 } & { \text { for } } & { x < - 2 } \\ { ( x - 1 ) ^ { 2 } - 2 } & { \text { for } } & { - 2 \leq x < 3 } \\ { - x + 5 } & { \text { for } } & { x \geq 3 } \end{array} \right.$

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 $x \geq 3$

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