Answer
$y$-intercept: $-\dfrac{1}{2}$
$x$-intercept: None
Work Step by Step
$r(x)=\dfrac{2}{x^{2}+3x-4}$
Substitute $r(x)$ by $y$:
$y=\dfrac{2}{x^{2}+3x-4}$
To find the $y$-intercept, set $x$ equal to $0$ and solve for $y$:
$y=\dfrac{2}{(0)^{2}+3(0)-4}=\dfrac{2}{-4}=-\dfrac{1}{2}$
To find the $x$-intercept, set $y$ equal to $0$ and solve for $x$:
$0=\dfrac{2}{x^{2}+3x-4}$
$(0)(x^{2}+3x-4)=2$
$0\ne2$ False
$y$-intercept: $-\dfrac{1}{2}$
$x$-intercept: None