Chapter 6.4, Problem 94E

To determine

To state: How the graph of $g(x)$ is related to the graph of $f(x)$

Answer to Problem 94E

the graph of $g(x)$ is a horizontal shrink of the graph of $f(x)$

Explanation of Solution

Given information:

The function is $g(x)=f(2x)$

Concept Used:

A nonrigid transformation of the graph of $y=f(x)$ is represented by

  $g(x)=cf(x)$ where the transformation is a vertical stretch if c>1 and a vertical shrink if 0 < c < 1 Another nonrigid transformation of the graph of $y=f(x)$ is represented by

  $h(x)=f(cx)$ Where the transformation is horizontal shrink if c>1 and a horizontal stretch if 0<c<1

Using the concept of transformation of graph,

It can be concluded that, the graph of $f(x)$ which is relative to the graph of $g(x)$ is a horizontal shrink of the graph of $f(x)$