Chapter 3.6, Problem 41E

To determine

To describe: the transformation from the graph of $f$ to the graph of $h$ .

Answer to Problem 41E

The translations are a vertical shrink by a factor of $\frac{1}{3}$ which is followed by a vertical translation 1 unit up.

Explanation of Solution

Given information:

Given functions

  $f\left(x\right)=x;h\left(x\right)=\frac{1}{2}x+1$

Calculation:

The functions are $f\left(x\right)=x;h\left(x\right)=\frac{1}{2}x+1$

The function $g$ is of the form $y=f\left(x\right)+k$ , where $k=1$

The graph of $\frac{1}{k}f\left(x\right)$ is a vertical shrink by a factor $\frac{1}{k}$ units of the graph of $f\left(x\right)$ .

The translations are a vertical shrink by a factor of $\frac{1}{3}$ which is followed by a vertical translation 1 unit up.