Answer
Refer to the graph below.
Work Step by Step
RECALL:
The graph of $y=a \cdot \sin{[b(x-d)]}$ has:
amplitude = $|a|$
period = $\frac{2\pi}{b}$
phase shift = $|d|$, to the left when $d\lt0$, to the right when $d\gt0$
The given function has:
$a=-\frac{1}{2}$
$b=4$
$d=-\frac{\pi}{2}$
Thus, the given function has:
amplitude = $|-\frac{1}{2}|=\frac{1}{2}$
period = $\frac{2\pi}{4} = \frac{\pi}{2}$
phase shift = $|-\frac{\pi}{2}|=\frac{\pi}{2}$ to the left
Therefore, the graph of the given function has the following properties/characteristics:
amplitude = $\frac{1}{2}$ so the y-values range from $-\frac{1}{2}$ to $\frac{1}{2}$
phase shift = $\frac{\pi}{2}$ units to the left
one period interval = $[-\frac{\pi}{2}, 0]$
Refer to the graph in the answer part above.