Summary (finding asymptotes)

Assume that is a rational function with

+...+

and

+...+

Concepts

x = c is a vertical asymptote if f(x) approaches infinity or negative infinity as x approaches c from the left or the right.

y = b is a horizontal asymptote if f(x) approaches b as x approaches infinity or negative infinity.

Finding Vertical Asymptotes

If c is a real number for which the denominator is zero but the numerator is not zero, then x = c is a vertical asymptote of the graph.

As x approaches c, f(x) approaches infinity or negative infinity.

Finding Horizontal Asymptotes

In the following, n is the degree of the numerator and k is the degree of the denominator of a rational function in lowest terms.

If n < k then y = 0 is the equation of the horizontal asymptote.

If n = k then is the equation of the horizontal asymptote. ( i.e. when the numerator and denominator have the same degree the horizontal asymptote is the ratio of the coefficients of the leading terms.)

If n>k then there is no horizontal asymptote.