Here are two different suggestions on how to vertically center image and table with respect to each other:

\documentclass[addpoints,12pt,answers]{exam}
\usepackage{graphicx}
\usepackage[export]{adjustbox}
\begin{document}
(a) On the left is the Cartesian plot of the function $y = 2 + 2 \cos (x)$ with
$0 \le x \le 2 \pi$. Using it, fill in the table, following the format
established in the first row.
\includegraphics[scale=0.5,valign=c]{example-image}
\begin{tabular}{l|l}
Range & Behavior of $2 + 2 \cos \theta$ \\
\hline
$\left( 0, \frac \pi 2 \right)$ & Decreasing from 2 to 0 \\
\hline
$\left(\frac \pi 2, \pi \right)$ & \\
\hline
$\left(\pi, \frac{3\pi}{2} \right)$ & \\
\hline
$\left(\frac{3\pi}{2}, 2\pi \right)$ &\\
\end{tabular}
\bigskip
(a) On the left is the Cartesian plot of the function $y = 2 + 2 \cos (x)$ with
$0 \le x \le 2 \pi$. Using it, fill in the table, following the format
established in the first row.
\begin{minipage}{0.475\textwidth}
\centering
\includegraphics[scale=0.5,valign=t]{example-image}
\end{minipage}
\hfill
\begin{minipage}{0.475\textwidth}
\centering
\renewcommand{\arraystretch}{1.5}
\begin{tabular}{l|l}
Range & Behavior of $2 + 2 \cos \theta$ \\
\hline
$\left( 0, \frac{\pi}{2} \right)$ & Decreasing from 2 to 0 \\
\hline
$\left(\frac{\pi}{2}, \pi \right)$ & \\
\hline
$\left(\pi, \frac{3\pi}{2} \right)$ & \\
\hline
$\left(\frac{3\pi}{2}, 2\pi \right)$ &\\
\end{tabular}
\end{minipage}
\end{document}
If you want to top align image and tabular, you can use
\includegraphics[scale=0.5,valign=t]{example-image}
\begin{tabular}[t]{l|l}
As a side note: Instead of manually numbering the subquestions, you might want to use the \parts
mechanism of the exam
class as shown below:
\documentclass[addpoints,12pt,answers]{exam}
\usepackage{graphicx}
\usepackage[export]{adjustbox}
\begin{document}
\begin{questions}
\question
This is the question text
\begin{parts}
\part On the left is the Cartesian plot of the function $y = 2 + 2 \cos (x)$ with
$0 \le x \le 2 \pi$. Using it, fill in the table, following the format
established in the first row.
\begin{minipage}{0.475\textwidth}
\centering
\includegraphics[scale=0.5,valign=t]{example-image}
\end{minipage}
\hfill
\begin{minipage}{0.475\textwidth}
\centering
\renewcommand{\arraystretch}{1.5}
\begin{tabular}{l|l}
Range & Behavior of $2 + 2 \cos \theta$ \\
\hline
$\left( 0, \frac{\pi}{2} \right)$ & Decreasing from 2 to 0 \\
\hline
$\left(\frac{\pi}{2}, \pi \right)$ & \\
\hline
$\left(\pi, \frac{3\pi}{2} \right)$ & \\
\hline
$\left(\frac{3\pi}{2}, 2\pi \right)$ &\\
\end{tabular}
\end{minipage}
\end{parts}
\end{questions}
\end{document}