### Home > PC3 > Chapter 2 > Lesson 2.2.3 > Problem2-81

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.

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

For $x<0$

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

For $x\ \ge0$

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

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