I have the function $f(x) = \frac {x^2-1}{x^2-4}$ that I need to graph.
This is what I found:
Vertical asymptotes: $x=2$ and $x=-2$
Horizontal asymptote: $y = 1$
$x$-intercepts: $x = 1$ and $x = -1$
$y$-intercept: $y = \frac 14$
Then I wanted to see if the function would ever cross the horizontal asymptote so I set the function equal to the asymptote and solved $1=\frac {x^2-1}{x^2-4}$ and I found that it doesn't cross the horizontal asymptote.
Then I set the function equal to the vertical asymptote and solved for $x$ so $2 = \frac {x^2-1}{x^2-4}$ and I got $x = -\sqrt 7$ and $x = +\sqrt 7$
I thought a line could never cross the vertical asymptotes so what are these values I got and how do I graph them?