How do you find the vertical, horizontal or slant asymptotes for #f(x)= (1)/(x^2-4)#?
The two vertical asymptotes are the vertical lines
The horizontal asymptote is the horizontal line
A function has vertical asymptotes where it is not defined. In this case we have a fraction, so the function is not defined where its denominator equals zero.
This means that we must ask that
So, the two vertical asymptotes are the vertical lines
A function has horizontal asymptotes if the limit as
So, the horizontal asymptote is the horizontal line
Note that both passages
Since the function has horizontal asymptotes, it can't have slant asymptotes. Actually, if we looked for slany asymptotes we would again find the line