# What determines the existence of a horizontal asymptote?

Apr 27, 2018

When you have a rational function with the degree of the numerator less than or equal to the denominator. ...

#### Explanation:

Given: How do you know a function has a horizontal asymptote?

There are a number of situations that cause horizontal asymptotes. Here are a couple:

A. When you have a rational function $\frac{N \left(x\right)}{D \left(x\right)}$ and the degree of the numerator is less than or equal to the degree of the denominator.

$\text{ " Ex. 1 " " f(x) = (2x^2 + 7x +1)/(x^2 -2x + 4) " } H A : y = 2$

$\text{ " Ex. 2 " " f(x) = (x +5)/(x^2 -2x + 4) " } H A : y = 0$

B. When you have an exponential function

$\text{ " Ex. 3 " " f(x) = 4^(x) " } H A : y = 0$

$\text{ " Ex. 4 " " f(x) = e^(2x) " } H A : y = 0$

C. Some of the hyperbolic functions (part of Calculus)