1. The problem asks which transformation maps the graph of $y=f(x)$ to $y=f(2x)$. 2. The general form of a horizontal transformation is $y=f(bx)$, where $b$ affects the horizontal stretch or compression. 3. If $|b|>1$, the graph compresses horizontally by a factor of $\frac{1}{|b|}$. If $0<|b|<1$, it stretches horizontally by a factor of $\frac{1}{|b|}$. 4. Here, $b=2$, so the graph of $y=f(2x)$ is a horizontal compression of the graph of $y=f(x)$ by a factor of $\frac{1}{2}$. 5. This means every point on the graph moves closer to the y-axis by half its original distance. 6. Therefore, the transformation is a horizontal compression by a factor of $\frac{1}{2}$.