Answer
The intercepts are: $(1,0)$, $(-1,0)$ and $(0, \dfrac{1}{4})$.
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.
Therefore, the intercepts of the function are:
The x-intercepts are when $y=0$, so we have:
$\dfrac{x^2-1}{x^2-4}=0 \\x^2-1=0\\x^2=1\\x=\pm1$
Now, the y-intercepts are when $x=0$, so we have:
$y=\dfrac{0^2-1}{0^2-4}=\dfrac{1}{4}$
Thus, the intercepts are: $(1,0)$, $(-1,0)$, and $(0, \dfrac{1}{4})$
