The function \( f(x) = \cos(2x) \) can be examined as a transformation of its parent function \( \cos(x) \).
The parent function \( \cos(x) \) has a period of \( 2\pi \). The function \( f(x) = \cos(2x) \) compresses the graph horizontally. Specifically, the period of \( f(x) \) is given by:
\[ \text{New Period} = \frac{2\pi}{2} = \pi. \]
This indicates a horizontal compression by a factor of \( \frac{1}{2} \).
Therefore, the correct response is:
The graph is a horizontal compression by a factor of \( \frac{1}{2} \).