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

1. Sketch the graph.

2. Use the graph to find the range and zeros of the function.

   Hint (b):

   Check the inequality signs carefully to see if the points are included or not.

3. Let $h\left(x\right) = f\left(x − 1\right)$. Sketch the graph of $h\left(x\right)$.

   Hint (c):

   Which way is the curve shifted; right, left, up, or down?

4. Write an expression for the piecewise function $h\left(x\right)$. Be sure to change the domain.

   Hint (d):

   1. Be careful when you substitute $\left(x − 1\right)$ in the second part. $2 − \left(x − 1\right)$ makes the expression $3 − x$.
   2. Check to make sure you shift your domain $1$ unit to the right.

5. Find the range and zeros of $h\left(x\right)$. How does this compare to your answer to part (b)?