Answer
The amplitude of the function is 3 and period is $\frac{\pi }{2}$
Work Step by Step
The given equation is in the form of $y=A\sin Bx$. Here, $A=3\text{ and }B=4$
So, the amplitude is:
$\begin{align}
& \text{Amplitude}=\left| A \right| \\
& =\left| 3 \right| \\
& =3
\end{align}$
The period is given below:
$\begin{align}
& \text{Period }=\frac{2\pi }{B} \\
& =\frac{2\pi }{4} \\
& =\frac{\pi }{2}
\end{align}$
$\text{Phase shift=}\frac{C}{B}=0$
And the quarter period is as follows:
$\begin{align}
& \text{Quarter-period}=\frac{\left( \frac{\pi }{2} \right)}{4} \\
& =\frac{\pi }{8}
\end{align}$
Now, add quarter periods starting from $x=0$ to generate x-values for the key points. The x-value for the first key point is as follows:
$x=\text{0}$
And the x-value for the second key point is:
$\begin{align}
& x=0+\frac{\pi }{8} \\
& =\frac{\pi }{8}
\end{align}$
And the x-value for the third key point is:
$\begin{align}
& x=\frac{\pi }{8}+\frac{\pi }{8} \\
& =\frac{\pi }{4}
\end{align}$
And the x-value for the fourth key point is:
$\begin{align}
& x=\frac{\pi }{4}+\frac{\pi }{8} \\
& =\frac{3\pi }{8}
\end{align}$
And the x-value for the fifth key point is:
$\begin{align}
& x=\frac{3\pi }{8}+\frac{\pi }{8} \\
& =\frac{\pi }{2}
\end{align}$
