Answer
(a) shift $f(x)$ right 4 units
(b) shift $f(x)$ down 4 units
Work Step by Step
(a) The graph $g(x)=(x-4)^{3}$ is obtained by shifting $f(x)=x^3$ right 4 units.
(b) The graph $g(x)=x^{3}-4$ is obtained by shifting $f(x)=x^3$ down 4 units.