How do you identify the vertical and horizontal asymptotes for rational functions?

1 Answer
Oct 30, 2014

How to Find Horizontal Asymptotes of Rational Functions

Let $f \left(x\right) = \frac{p \left(x\right)}{q \left(x\right)}$, where p(x) is a polynomial of degree $m$ with leading coefficient $a$, and q(x) is a polynomial of degree $n$ with leading coefficient $b$. There are three cases:

Case 1: If $m > n$, then $f$ has no horizontal asymptotes.
Case 2: If $m = n$, then $y = \frac{a}{b}$ is the horizontal asymptote of $f$.
Case 3: If $m < n$, then $y = 0$ is the horizontal asymptote of $f$.

How to Find Vertical Asymptotes of Rational Functions

If there are any common factors between the numerator and the denominator, then cancel all common factors. Set the denominator equal to zero then solve for $x$.

I hope that this was helpful.