next up previous
Next: Critical Points Up: Graphs of Functions Previous: Zeros of Functions

Asymptotes

If you remember, an asymptote is a limiting value which the function approaches but does not necessarily reach. There are three types of asymptotes, horizontal, vertical and slant.

A horizontal asymptote is a line y = c such that either tex2html_wrap_inline226 or tex2html_wrap_inline228 . It is possible for a function to cross a horizontal asymptote.

A vertical asymptote is a line x = c such that the function f is undefined at x = c. A function can never cross a vertical asymptote.

A slant asymptote is more complicated. If y = f(x) is a rational function, the the polynomial portion of the quotient obtained through long division defines a straight line which the rational function is asymptotic to.



Vector Calculus
Wed Sep 17 14:50:13 MST 1997