Question

use transformations of the standard cubic function, f(x)=x³, to graph the function h(x)=\frac{1}{2}x³. what transformation is needed to graph the function h(x)=\frac{1}{2}x³? choose the correct answer below. a. the graph of f(x)=x³ should be vertically stretched by a factor of \frac{1}{2}. b. the graph of f(x)=x³ should be vertically shrunk by a factor of \frac{1}{2}. c. the graph of f(x)=x³ should be horizontally...

Explanation:

For a function $g(x) = a \cdot f(x)$ where $0 < |a| < 1$, the graph of $f(x)$ undergoes a vertical shrink by a factor of $a$. Here, $h(x)=\frac{1}{2}x^3 = \frac{1}{2}f(x)$ with $0 < \frac{1}{2} < 1$, so it is a vertical shrink by $\frac{1}{2}$.

Answer:

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