Answer
The intercepts of the function are: $(0,-8), (2, 0)$
Work Step by Step
In order to solve this problem, we will have to recall the following points:
(a) The intercepts of a function are those points where the graph crosses the $x-$ axis or the $y-$ axis.
(b) We set $y=0$ and then solve for $x$ in order to calculate the x-intercept.
(c) We set $x=0$ and then solve for $y$ in order to calculate the y-intercept.
Case: 1 Let $y=0$ and the solve for $x$ to obtain:
$y=x^3-8 \\ 0=x^3-8 \implies x =2$
Case: 2 Let $x=0$ and the solve for $y$ to obtain:
$y=x^3-8 \\ y=0^3-8 \implies y=-8$
Therefore, the intercepts of the function are: $(0,-8), (2, 0)$
