Answer
See graph below.
Work Step by Step
The question ONLY asks for a graph of the polar equation.
Given $r = \sqrt 3 + \cos θ$
Table of Values:
$(\sqrt 3 + 1, 0)$
$(\sqrt 3 + 1/2, \frac{\pi}{3})$
$(\sqrt 3, \frac{\pi}{2})$
$(\sqrt 3 - 1/2, \frac{2\pi}{3})$
$(\sqrt 3 - 1, \pi)$
$(\sqrt 3 - 1/2, \frac{4\pi}{3})$
$(\sqrt 3, \frac{3\pi}{2})$
$(\sqrt 3 + 1/2, \frac{5\pi}{3})$
See graph below. It is in the shape of a cardoid.