Question

Describe the graph of the function f(x)=cos(2x)
as a transformation of its parent function.(1 point)
Responses

The graph is a horizontal compression by a factor of 12
.
The graph is a horizontal compression by a factor of Start Fraction 1 over 2 End Fraction .

The graph is a vertical compression by a factor of 12
.
The graph is a vertical compression by a factor of Start Fraction 1 over 2 End Fraction .

The graph is a horizontal stretch by a factor of 2.
The graph is a horizontal stretch by a factor of 2.

The graph is a vertical stretch by a factor of 2.
The graph is a vertical stretch by a factor of 2.

Answer 1

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 \( \frac{1}{2} \).**