How to Find the Horizontal Asymptote

by Rick H

Finding the horizontal asymtote is a bit more tricky then just the simple vertical asymtote. You have to take to consideration a couple of things before you can find the horizontal asymptote of a rational function.

Thos considerations are as follows

$\frac { { polynomial }^{ n } }{ { polynomial }^{ n } }$

  • If the degree of the polynomial on the numerator is less than the degree of the polynomial in the denominator then the Horizontal asymptote will always be at

$y=0$

  • If the degree of the polynomial on the numerator is equal to the degree of the polynomial in the denominator then find the leading coefficients of both polynomials and reduce them to get the horizontal asymptote.

$y = \frac { { 3x }^{ 2 } }{ { 2x }^{ 2 } }$ $y = \frac { 3 }{ 2}$

  • If the degree on the numerator is greater than the degree of the denominator then you wil have no horizontal asymtote. You will have an oblique asymptote.

Summary:

$\frac { { polynomial }^{ n } }{ { polynomial }^{ n } }$ $ n < n \ then \ y=0$ $ n == n \ then \ y=\frac { { p }^{ n } }{ { p }^{ n } }$ $ n > n \ then \ No \ Horizontal \ Asymptote$