Answer
d)
Work Step by Step
If C is any real number and $B> 0$, then the graphs of $y = k + A\sin(Bx+C)$ and $y = k + A\cos (Bx+C)$ will have
$Amplitude = |A|$
$Period = \frac{2\pi}{B}$
$Horizontal\ shift = –\frac{C}{B}$
$Vertical\ shift = k$
so for $y = 2 + \cos (\frac{\pi}{2} x - \frac{\pi}{2} )$
$Amplitude = |1| = 1 $
$Period = \frac{2\pi}{\frac{\pi}{2}} = 4$
$Horizontal\ shift = (–\frac{-\frac{\pi}{2}}{\frac{\pi}{2}}) = 1$ i.e right shift $1$
$Vertical\ shift = 2$ ($2$ upward shift)
At $x = 0, y = 2$
At $x = 1, y = 3$
So d) is the correct answer