Answer
The Amplitude is $ 0.5$
The Period is $ 2$
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: $\frac{2\pi} {|c|}$,
Given $y = 1+ 0.5 \cos (\pi x)$
The Amplitude is $|0.5| = 0.5$
The Period is $\frac{2\pi}{|\pi|} = 2$
The transformations are as follows
The blue graph represents the graph of $\cos x$
The red graph represents the graph of the given function that compressed horizontally by a factor of $ \pi$, stretched vertically by a factor of $0.5$, and shifted up 1 unit
See graph below.