#### Answer

See graph and explanations.

#### Work Step by Step

Step 1. Graph the function $f(x)=x^3$, shown as the blue curve in the figure.
Step 2. To obtain the graph of function $r(x)=\frac{1}{4}x^3-1$, shrink the original vertically by a factor of 4, then shift the result vertically 1 unit down, shown as the red curve in the figure.