Chapter 4.4, Problem 49E

Solution

To state: The transformation required to obtain the graph of $y_2=\frac{5}{3}\cos 2x$ from the graph of $y_1=\cos 2x$ .

The graph of $y_2$ is a vertical stretch of $y_1$ by a factor of $\frac{5}{3}$ .

Given information:

The given function are $y_2=\frac{5}{3}\cos 2x\text{ and }{y}_1=\cos 2x$ .

Explanation:

Now consider the given function: $y_2=\frac{5}{3}\cos 2x\text{ and }{y}_1=\cos 2x$

To describe how the graphs are related, compare the amplitude and period of these functions.

The amplitudes for $y_2\text{ is }\frac{5}{3}\text{ and }{y}_1\text{ is 1}$ .

The amplitude will determine if the graph will stretch or shrink vertically.

If the amplitude is greater than 1, the graph stretches with respect to y- axis.

If the amplitude is less than 1, the graph shrinks with respect to y- axis.

Thus the graph of $y_2=\frac{5}{3}\cos 2x$ is vertical stretch of graph of $y_1=\cos 2x$ by a factor of $\frac{5}{3}$ .