Answer
$y$-intercept: $2$
$x$-intercept: $-2$
Work Step by Step
$r(x)=\dfrac{x^{3}+8}{x^{2}+4}$
Substitute $r(x)$ by $y$:
$y=\dfrac{x^{3}+8}{x^{2}+4}$
To find the $y$-intercept, set $x$ equal to $0$ and solve for $y$:
$y=\dfrac{(0)^{3}+8}{(0)^{2}+4}=\dfrac{8}{4}=2$
To find the $x$-intercept, set $y$ equal to $0$ and solve for $x$:
$0=\dfrac{x^{3}+8}{x^{2}+4}$
$(0)(x^{2}+4)=x^{3}+8$
$x^{3}+8=0$
$x^{3}=-8$
$\sqrt[3]{x^{3}}=\sqrt[3]{-8}$
$x=-2$
$y$-intercept: $2$
$x$-intercept: $-2$
