### Home > PC3 > Chapter 12 > Lesson 12.1.5 > Problem12-80

12-80.

For the piecewise-defined function below, complete the following problems.

$f ( x ) = \left\{ \begin{array} { l l } { - 2 x + 3 } & { \text { for } - 2 \leq x < 2 } \\ { ( x - 2 ) ^ { 2 } - 1 } & { \text { for } \quad 2 \leq x < 5 } \end{array} \right.$

1. Graph the function. Clearly scale and draw your axes.

1. Graph the height at $2$ for each function first.
2. Fill in the graph from $−2$ to $2$ with the first part.
3. Fill in the graph from $2$ to $5$ with the second part.
4. Check all end-points.

2. Let $g(x) = f (x + 2) − 3$. Graph this function, $g\left(x\right)$, and specify its domain.

$g(x)$ is shifted to the left $2$ units and down $3$ units.