Graph the function $y=3 \cos \left(\frac{1}{4} x\right)$. Give the period and the amplitude.
Choose the correct graph of the function.
A.
B.
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D.
The amplitude is (Simplify your answer: Type an exact answer, using $\pi$ as needed.)
The period is
(Simplify your answer. Type an exact answer, using $\pi$ as needed.)

Step 1 ：First, we need to identify the amplitude and the period of the function $y=3 \cos \left(\frac{1}{4} x\right)$.

Step 2 ：The amplitude of the function is the absolute value of the coefficient of the cosine function. In this case, the amplitude is $\boxed{3}$.

Step 3 ：The period of the function is determined by the coefficient of $x$ inside the cosine function. The graph of $y=\cos \left(\frac{1}{4} x\right)$ passes through one full period as $\frac{1}{4}x$ ranges from $0$ to $2\pi$, which means $x$ ranges from $0$ to $\boxed{8\pi}$.

Step 4 ：Finally, we can graph the function. The graph will have a maximum value of $3$ and a minimum value of $-3$, and it will repeat every $8\pi$ units.