# HOW TO FIND HORIZONTAL ASYMPTOTE OF A FUNCTION

In this section, you will learn how to find horizontal asymptote of a function. .

We will be able to find horizontal asymptotes of a function, only if it is a rational function.

That is, the function has to be in the form of

f(x)  =  g(x) / h(x)

Rational Function - Example :  ## Steps to Find Horizontal Asymptotes of a Rational Function

Let f(x) be the given rational function. Compare the highest exponent of the numerator and denominator.

Case 1 :

If the highest exponent of the numerator and denominator are equal, equation of horizontal asymptote is

y  =  a / b

Here a and b are the coefficients of highest exponent terms at the numerator and denominator respectively.

Case 2 :

If the highest exponent of the numerator is less than the highest exponent of the denominator, equation of horizontal asymptote is

y  =  o  (or)  x-axis

Case 3 :

If the highest exponent of the numerator is greater than the highest exponent of the denominator, there is no horizontal asymptote and there is only slant asymptote or oblique.

## Examples

Example 1 :

Find the equation of horizontal asymptote for the function given below.

f(x)  =  1 / (x + 6)

Solution :

Step 1:

In the given rational function, the highest exponent of the numerator is 0 and the highest exponent of the denominator is 1.

Step 2 :

Clearly highest exponent of the numerator is less than the highest exponent of the denominator.

Hence, equation of the horizontal asymptote is

y  =  0  (or)  x-axis

Example 2 :

Find the equation of horizontal asymptote for the function given below.

f(x)  =  (x2 + 2x - 3) / (x2 - 5x + 6)

Solution :

Step 1 :

In the given rational function, the highest exponent of the numerator is 2 and the highest exponent of the denominator is 2.

Step 2 :

Clearly, the exponent of the numerator and the denominator are equal.

Step 3 :

Now, to get the equation of the horizontal asymptote, we have to divide the coefficients of highest exponent terms of the numerator and denominator.

So, equation of the horizontal asymptote is

y  =  1 / 1

y  =  1

Example 3 :

Find the equation of horizontal asymptote for the function given below.

f(x)  =  (x2 - 4) / (2x - 3)

Solution :

Step 1 :

In the given rational function, the highest exponent of the numerator is 2 and the highest exponent of the denominator is 1.

Step 2 :

Clearly, the exponent of the numerator is greater than the exponent of the denominator.

Step 3 :

As per the steps explained above, there is no horizontal asymptote. Apart from the stuff given aboveif you need any other stuff in math, please use our google custom search here.

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