the graph of $f(x)$ is shown. which graph represents $g(x)=f(2x)$?
the graph of $f(x)$ is shown. which graph represents $g(x)=f(2x)$?
Answer
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 - values 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 - values of the corresponding key - points of $y = f(2x)$. The y - values remain the same.
Answer:
The graph that has the same shape as the graph of $f(x)$ but is horizontally compressed towards the y - axis by a factor of $\frac{1}{2}$. Without specific labels on the options, it's not possible to identify the exact option by letter, but it should be the graph where all x - coordinates of the features of $f(x)$ are halved while y - coordinates stay the same.