Answer
The amplitude of the function is $3$, period is $6$, and phase shift is $9$.
Work Step by Step
The given equation is in the form of $y=A\sin \left( Bx-C \right)$.
Here, $A=-3,\text{ }B=\frac{\pi }{3}\text{ and }C=3\pi $
So, the amplitude is:
$\begin{align}
& \text{Amplitude=}\left| A \right| \\
& =\left| -3 \right| \\
& =3
\end{align}$
The period is given below:
$\begin{align}
& \text{Period = }\frac{2\pi }{B} \\
& =\frac{2\pi }{\left( \frac{\pi }{3} \right)} \\
& =6
\end{align}$
The phase shift is:
$\begin{align}
& \text{Phase shift = }\frac{C}{B} \\
& =\frac{3\pi }{\left( \frac{\pi }{3} \right)} \\
& =9
\end{align}$
And the quarter period is as follows:
$\begin{align}
& \text{Quarter-period}=\frac{6}{4} \\
& =\frac{3}{2}
\end{align}$
Now, add quarter periods starting from $x=9$ to generate x-values for the key points. The x-value for the first key point is as follows:
$x=9$
And the x-value for the second key point is:
$\begin{align}
& x=9+\frac{3}{2} \\
& =\frac{21}{2}
\end{align}$
And the x-value for the third key point is:
$\begin{align}
& x=\frac{21}{2}+\frac{3}{2} \\
& =12
\end{align}$
And the x-value for the fourth key point is:
$\begin{align}
& x=12+\frac{3}{2} \\
& =\frac{27}{2}
\end{align}$
And the x-value for the fifth key point is:
$\begin{align}
& x=\frac{27}{2}+\frac{3}{2} \\
& =15
\end{align}$
