find the amplitude of the sinusoidal function.\nsimplify any fractions.

Explanation:

Step1: Recall amplitude definition

The amplitude of a sinusoidal function is half the vertical distance between the maximum and minimum values.

Step2: Identify max and min

From the graph, the maximum value of the function $f(x)$ is $4$ and the minimum value is $- 4$.

Step3: Calculate amplitude

The vertical distance between the maximum and minimum is $4-(-4)=8$. Then the amplitude $A=\frac{4 - (-4)}{2}=\frac{8}{2}=4$.

Answer:

$4$