# How to Horizontal Asymptote of a Rational Equation - Definition, Example

## How to Horizontal Asymptote of a Rational Equation - Tutorial

#### Definition:

An asymptote is a line that a graph approaches, but does not intersect. Horizontal asymptote of rational equation can be found when the highest degree of polynomial is equal in both the numerator and denominator.

#### Method 1:

When the line y = L , then its called as horizontal asymptote of the curve y = f(x) if either #### Method 2:

For the rational function, f(x)

If the polynomial degree of x in the numerator is equal to the polynomial degree of x in the denominator , then y = c. Value of c can be obtained by dividing the leading coefficients.

If the polynomial degree of x in the numerator is less than the polynomial degree of x in the denominator then y = 0. This is called as horizontal asymptote.

#### Example:

Find the horizontal asymptotes of the following function. #### Method 1:

Divide both numerator and denominator by x. The line y = 2/ 3 is the horizontal asymptote.

#### Method 2:

The polynomial degree of x in the numerator is equal to the polynomial degree of x in the denominator.

Then dividing the leading coefficients we get 2/3.

The line y = 2/ 3 is the horizontal asymptote.