#### Answer

$\text{I}$

#### Work Step by Step

RECALL:
The graph of $y=c+a\cdot\cos{x}$ involves a either a vertical shift of $c$ units upward (when $c\gt0$) or $|c|$ units downward when $c\lt0$ of the parent function $f(x)=\cos{x}$.
The given function, $y=1+\cos{x}$, has $c=1$ so it involves a $1$-unit shift upward of the parent function $f(x)=\cos{x}$.
Recall that the graph of $y=\cos{x}$ contains the points $(0, 1), (\pi, -1),$ and $(2\pi, 1)$.
This means that when the graph of $f(x)=\cos{x}$ is shifted $1$ unit upward, the resulting graph contains the points $(0, 2), (\pi, 0),$ and $(2\pi, 2)$.
Note that the only graph among thae choices that contains the three points above is the one in Option $I$.