### Home > PC3 > Chapter 1 > Lesson 1.2.3 > Problem1-96

1-96.

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

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.

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

For $x<-2$

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

For $x\geq -2$

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

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