# How do you find the horizontal asymptote of a curve?

##### 1 Answer

To find the horizontal asymptote (generally of a rational function), you will need to use the Limit Laws, the definitions of limits at infinity, and the following theorem:

Recall from the definition of limits that we can only take limits of real numbers and infinity is not a real number, which is why we need the previous theorem.

The strategy for using the theorem is to divide every term by the highest power term from the denominator; this should leave us with a polynomial in the numerator or a constant. If we have a polynomial, then there is no horizontal asymptote. If we have a constant, then y=constant is our horizontal asymptote.

For example:

We divded every term by

Now use our limit laws.

Now simplify.

Finally use the theorem and the limit law of a constant.

So, in this case we have a horizontal asymptote of

If we ended up with

The theorem @

This is the general strategy, obviously more difficult questions can be framed and you should read your textbook for those examples.