Chapter 1.2, Problem 22E

To determine

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

Answer to Problem 22E

Transformed function is $g(x)=6-3x$ .

Explanation of Solution

Given information: Function is $f(x)=6-x$ .

Calculation:

Since x-intercept of $f$ is $6$ and x-intercept of $g$ is $2$ , so analyzing the ratio of abscissas, there is a horizontal shrink by a factor of $\frac{1}{3}$ , so

  $\begin{array}{l}g(x)=f(3x)\\ g(x)=6-3x\end{array}$

Hence, transformed function is $g(x)=6-3x$ .

Graph:

  

Black line represents transformed function $g$ and violet line represents initial function $f$ .

Thus, the graph from graphing calculator verifies the answer.