the graph of (f(x)) is shown. which graph represents (g(x)=f(2x)?)

Explanation:

Step1: Recall horizontal - compression rule

For a function $y = f(bx)$ where $b>1$, the graph of $y = f(x)$ is horizontally compressed by a factor of $\frac{1}{b}$. Here $b = 2$, so the graph of $y=f(x)$ is horizontally compressed by a factor of $\frac{1}{2}$.

Step2: Analyze key - points

The x - coordinates of the key - points (such as x - intercepts, y - intercepts, and turning points) of $y = f(x)$ are divided by 2 to get the x - coordinates of the corresponding key - points of $y = f(2x)$. The y - coordinates remain the same.

Answer:

The graph that has the same general shape as the graph of $f(x)$ but is horizontally compressed towards the y - axis. Without seeing the specific options clearly, the correct graph will have all its horizontal features (like the distance between peaks, valleys, and intercepts) halved compared to the graph of $f(x)$.