CPM Homework Help : PC3 Problem 1-96

Graph each piecewise-defined function given below and determine whether the function is continuous.

Hint:

Make a table of value for each function. Be careful at the point where the graph changes. Will the point exist or not exist for each part? Then graph.

$f ( x ) = \left\{ \begin{array} { l l } { x + 4 } & { \text { for } x < - 2 } \\ { \frac { 1 } { 2 } x ^ { 2 } } & { \text { for } x \geq - 2 } \end{array} \right.$
Hint (a):
For $x<-2$
$x$
$f\left(x\right)=x+4$
$-5$
$-4$
$-3$
$-2$
For $x\geq -2$
$x$
$f\left(x\right)=\frac{1}{2}x^2$
$-2$
$-1$
$0$
$1$

$g ( x ) = \left\{ \begin{array} { l l } { x + 4} & {\text { for } x \geq 3 } \\ { \frac { 1 } { 2 } x ^ { 2 } } & { \text { for } x < 3 } \end{array} \right.$

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

$x$	$f\left(x\right)=\frac{1}{2}x^2$
$-2$
$-1$
$0$
$1$