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.


How to determine the horizontal Asymptote?

Method 1:

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


Horizontal Asymptote Curve

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.


Asymptotes Function

Method 1:

Divide both numerator and denominator by x.


Horizontal Asymptote

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.

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