Question

use transformations of the standard cubic function, f(x)=x³, to graph the function h(x)=\frac{1}{2}x³. the graph of f(x)=x³ should be vertically shrunk by a factor of \frac{1}{2}. the graph of f(x)=x³ should be horizontally shrunk by a factor of \frac{1}{2}. the graph of f(x)=x³ should be horizontally stretched by a factor of \frac{1}{2}.

Explanation:

Step1: Recall vertical scaling rule

For a function $g(x) = a \cdot f(x)$ where $0 < |a| < 1$, the graph of $f(x)$ is vertically shrunk by a factor of $\frac{1}{|a|}$.

Step2: Match to given function

Here, $h(x) = \frac{1}{2}x^3 = \frac{1}{2}f(x)$, so $a = \frac{1}{2}$. The vertical shrink factor is $\frac{1}{\frac{1}{2}} = 2$? No, correction: For $h(x)=a f(x)$, when $0

Answer:

The graph of $f(x)=x^3$ should be vertically shrunk by a factor of $\frac{1}{2}$.