Chapter 4.5, Problem 14E

To determine

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

Explanation of Solution

Given information:

Given functions are

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

Concept used:

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

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

Calculation:

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

The amplitude of the function $f\left(x\right)=\sin x$ is 1 and amplitude of the function $g\left(x\right)=2\sin x$ is 2.

Therefore, the amplitude of $g\left(x\right)$ is 2 times more than the amplitude of $f\left(x\right)$ .

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

Therefore, both functions have the same period.

Draw the graph of the functions $f\left(x\right)$ and $g\left(x\right)$ on a same rectangular coordinate system a follows: