Answer
$f(x)=\frac{1}{4}x^3$
Work Step by Step
Since $f(x)=x^3$ is the overall shape of the graph we will start with that:
$f(x)=x^3$
Notice that the graph has been compressed vertically (by a factor of k). The function of the graph can be written as:
$f(x)=kx^3$
Substitute in the point (2,2) to solve for k:
$2=k(2^3)$
$2=k(8)$
$k=\frac{2}{8}=\frac{1}{4}$
So, the final equation:
$f(x)=\frac{1}{4}x^3$
