CPM Homework Help : PC Problem 4-44

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

Steps:

1. Find the height at $0$ for both parts of the piece-wise function.
2. If they are the same, it is continuous.
3. Plot the points found above and continue with the appropriate graph on either side.

Graph:

Piecewise, left curve coming from lower left, concave down, ending with open point on the positive y axis, right curve, starting at closed point on negative y aixs, concave up, continuing up & right.