Chapter 4.5, Problem 15E

To determine

To describe: the relationship between the graphs of $f$ and $g$ .

Explanation of Solution

Given information:

Given functions are

  $\begin{array}{l}f\left(x\right)=\cos 2x\\ g\left(x\right)=-\cos 2x\end{array}$

Concept used:

For the standard equation is $y=a\cos bx$ .

Amplitude is $\left|a\right|$ and period is $\frac{2\pi }{b}$ .

Calculation:

Consider the function $f\left(x\right)=\cos 2x$ and $g\left(x\right)=-\cos 2x$ .

The amplitude of the function $f\left(x\right)=\cos 2x$ is 1 and amplitude of the function $g\left(x\right)=-\cos 2x$ is 1. Therefore, both functions have same amplitude.

The period of the function $f\left(x\right)=\cos 2x$ is $\pi$ and period of the function $f\left(x\right)=\cos 2x$ is $\pi$ .

Therefore, both functions have same period.

Let us first plot the graph of $f\left(x\right)=\cos 2x$

  

Now plotting the graph of $g\left(x\right)=-\cos 2x$

  

While observing at the two graphs, it is clear that $g$ is a reflection of $f$ in the $x$ -axis.