CPM Homework Help : PC3 Problem 2-81

Sketch the graph of $f(x) =\left\{ \begin{array} { c } { - x ^ { 2 } + 4 \text { for } x < 0 } \\ { x ^ { 2 } - 1 \text { for } x \geq 0 } \end{array} \right.$ . Is $y=f(x)$ continuous? Explain.

Step:

Copy and complete the following table. Then graph the points.

For $x<0$

$x$	$-x^2+4$
$-3$
$-2$
$-1$
$0$

For $x\ \ge0$

$x$	$x^2-1$
$0$
$1$
$2$
$3$

More Help:

Can the curve be traced from left to right without lifting your pencil?
If so, then it is continuous.