Refer to the blue graph below.
Work Step by Step
The parent function of $y=(x-2)^3$ is $y=x^3$. Note that in $y=x^3$, when $x$ is replaced by $x-2$, the function becomes $y=(x-2)^3$. This means that with $y=f(x)=x^3$ as the parent function, the given function is equivalent to $y=f(x-2)$. RECALL: The graph of $y=f(x-c)$ involves a horizontal shift of $c$ units to the right of the parent function $y=f(x)$. Thus, to graph the given function, perform the following steps: (1) Graph the parent function $y=x^3$. Refer to the black graph below. (2) With $c=2$, shift the graph of $y=x^3$ two units to the right to obtain the graph of $y=(x-2)^3$. Refer to the blue graph below.