Answer
The Amplitude is $|1| = 1$
The Period is $\frac{2\pi}{|3|} = \frac{2\pi}{3}$
The Horizontal shift is $\frac {\pi}{6}$ units to the left
See graph below.
Work Step by Step
For $y=a\sin c(x−h) + k$ $y =a \cos c(x−h) + k$,
Amplitude: $|a|$, Period: $\frac{2\pi} {|c|}$,
Horizontal Shift: h
The question asks for a graph, amplitude, period, and horizontal shift of the function.
Given $y = \cos (3x + \frac{\pi}{2}) + 1$
$y = \cos 3(x + \frac{\pi}{6}) + 1 $
The Amplitude is $|1| = 1$
The Period is $\frac{2\pi}{|3|} = \frac{2\pi}{3}$
The Horizontal shift is $\frac {\pi}{6}$ units to the left
See graph below.