### Home > PC3 > Chapter 6 > Lesson 6.1.2 > Problem6-38

6-38.

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 a graph of $y = f\left(x\right)$.

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

The zeros are the $x$-intercepts on the graph.
The range is the set of all output values.

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

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

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

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. What are the range and zeros of $h$? How does this compare to your answer to part (b)? Explain.

Review the hint in part (b).