### Home > PC > Chapter 3 > Lesson 3.1.1 > Problem3-14

3-14.

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.

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 $h\left(x\right)$.

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.

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)?