Answer
Refer to the graph below.
Work Step by Step
RECALL:
The graph of $y=a \cdot \cos{[b(x-d)]}$ has:
amplitude = $|a|$
period = $\frac{2\pi}{b}$
phase shift = $|d|$, to the left when $d\lt0$, to the right when $d\gt0$
Write the given function in the form $y=a \cdot \cos{[b(x-d)]}$ by factoring out $4$ inside the cosine function to obtain:
$y=3\cos{[4(x+\frac{\pi}{4})]}$
The given function has:
$a=3$
$b=4$
$d=-\frac{\pi}{4}$
Thus, the given function has:
amplitude = $|3|=3$
period = $\frac{2\pi}{4} = \frac{\pi}{2}$
phase shift = $|-\frac{\pi}{4}|=\frac{\pi}{4}$ to the left
Therefore, the graph of the given function has the following properties/characteristics:
amplitude = $3$ so the y-values range from $-3$ to $3$
phase shift = $\frac{\pi}{2}$ units to the right
one period interval = $[\frac{-\pi}{4}, \frac{\pi}{4}]$
Refer to the graph in the answer part above.