Answer
Both functions have the same amplitudes and periods but the graph of function $g$ is a vertical shift of $2$ units down of function $f$.
Work Step by Step
Using the equation of sine $y=a\cos b(x-c)+d$:
For $f(x)=\cos 4x=1\cos 4(x-0)+0$,
$a=1$
$period=\frac{2\pi}{b}=\frac{2\pi}{4}=\frac{\pi}{2}$
$horizontal~shift=c=0=none$
$vertical~shift=d=0=none$
For $g(x)=-2+\cos 4x=1\cos 4(x-0)-2$,
$a=1$
$period=\frac{2\pi}{b}=\frac{2\pi}{4}=\frac{\pi}{2}$
$horizontal~shift=c=0=none$
$vertical~shift=d=-2$
Thus, both functions have the same amplitudes and periods but the graph of function $g$ is a vertical shift of $2$ units down of function $f$.
