Answer
The amplitude of the function is $3$, period is $2\pi $ and phase shift is $-\pi $
Work Step by Step
The given equation is in the form of $y=A\cos \left( Bx-C \right)$.
Here, $A=-3,\text{ }B=1\text{ and }C=-\pi $
So, the amplitude is:
$\begin{align}
& \text{Amplitude}=\left| A \right| \\
& =\left| -3 \right| \\
& =3
\end{align}$
The period is given below:
$\begin{align}
& \text{Period = }\frac{2\pi }{B} \\
& =\frac{2\pi }{1} \\
& =2\pi
\end{align}$
The phase shift is:
$\begin{align}
& \text{Phase shift = }\frac{C}{B} \\
& =\frac{-\pi }{1} \\
& =-\pi
\end{align}$
And the quarter period is as follows:
$\begin{align}
& \text{Quarter-period}=\frac{2\pi }{4} \\
& =\frac{\pi }{2}
\end{align}$
Now, add quarter periods starting from $x=-\pi $ to generate x-values for the key points. The x-value for the first key point is as follows:
$x=-\pi $
And the x-value for the second key point is:
$\begin{align}
& x=-\pi +\frac{\pi }{2} \\
& =-\frac{\pi }{2}
\end{align}$
And the x-value for the third key point is:
$\begin{align}
& x=-\frac{\pi }{2}+\frac{\pi }{2} \\
& =0
\end{align}$
And the x-value for the fourth key point is:
$\begin{align}
& x=0+\frac{\pi }{2} \\
& =\frac{\pi }{2}
\end{align}$
And the x-value for the fifth key point is:
$\begin{align}
& x=\frac{\pi }{2}+\frac{\pi }{2} \\
& =\pi
\end{align}$
