Chapter 1.2, Problem 28E

To determine

To write: A function $g$ whose graph represents the indicated transformations of the graph of $f$ .

Answer to Problem 28E

The function is $g(x)=\frac{x}{3}-1$ .

Explanation of Solution

Given information: Function is $f(x)=x$ .

Calculation:

Translating $3$ units down,

  $\begin{array}{l}h(x)=f(x)-3\\ h(x)=x-3\end{array}$

Shrinking vertically by a factor of $\frac{1}{3}$ ,

  $\begin{array}{l}g(x)=\frac{1}{3}h(x)\\ g(x)=\frac{1}{3}(x-3)\\ g(x)=\frac{x}{3}-1\end{array}$

Thus, the function is $g(x)=\frac{x}{3}-1$ .