Answer
The amplitude and period of the function are $2$ and $8\pi $ , respectively.
Work Step by Step
We have the trigonometric function
$y=2\sin \frac{1}{4}x$
The amplitude is the maximum value of $y$. The maximum value of the given trigonometric function is $2$. So, the amplitude of the trigonometric function is $2$.
The function after a certain interval starts repeating itself, and this interval is known as the period of the function.
And the period $\left( B \right)$ of the trigonometric function is
$\begin{align}
& B=\frac{2\pi }{\left( \frac{1}{4} \right)} \\
& =8\pi
\end{align}$
And the quarter period is $\frac{8\pi }{4}$ or $2\pi $. The cycle begins at $x=0$. Add quarter periods to find out the key points.
First key point is
${{x}_{1}}=0$
Second key point is
$\begin{align}
& {{x}_{2}}=0+2\pi \\
& =2\pi
\end{align}$
Third key point is
$\begin{align}
& {{x}_{3}}=2\pi +2\pi \\
& =4\pi
\end{align}$
Fourth key point is
$\begin{align}
& {{x}_{4}}=4\pi +2\pi \\
& =6\pi
\end{align}$
Fifth key point is
$\begin{align}
& {{x}_{5}}=6\pi +2\pi \\
& =8\pi
\end{align}$
