what does the transformation $f(x)\to f(\frac{1}{2}x)$ do to the graph of $f(x)$?\nshrinks it…

Explanation:

Step1: Recall function - transformation rule

For a function $y = f(x)$ and a transformation $y = f(bx)$ where $b>0$, if $b > 1$, the graph of $y = f(x)$ is shrunk horizontally by a factor of $\frac{1}{b}$, and if $0 < b<1$, the graph of $y = f(x)$ is stretched horizontally by a factor of $\frac{1}{b}$. In the transformation $f(x)\to f(\frac{1}{2}x)$, we have $b=\frac{1}{2}$ with $0 < b<1$.

Step2: Determine the transformation type

Since $b = \frac{1}{2}$ and $0<\frac{1}{2}<1$, the graph of $f(x)$ is stretched horizontally by a factor of $\frac{1}{\frac{1}{2}}=2$.

Answer:

stretches it horizontally