Answer
x-intercept: $-2$.
y-intercept: $2$.
Work Step by Step
The y- intercept is the value $r(0)$, if defined.
$r(0)=\displaystyle \frac{0+8}{0+4}=2 $
The x intercepts are values of x where $r(x)=0.$
$r(x)=0$ occurs when the numerator equals 0.
The numerator is zero when
$x^{3}+8=0$
$x^{3}=-8$
$x=-2$
