# What is rational function and how do you find domain, vertical and horizontal asymptotes. Also what is "holes" with all limits and continuity and discontinuity?

##### 1 Answer

A rational function is where there are

The part under the bar is called the *denominator* .

This puts limits on the domain of

Simple example: *domain* :

This also defines the *vertical asymptote*

It makes a difference whether you move toward the

We say

So there is a *discontinuity*

graph{1/x [-16.02, 16.01, -8.01, 8.01]}

On the other hand: If we make *horizontal asymptote*

We say

Of course ratinal functions are usually more complicated, like:

In the latter example there are even two vertical asymptotes, as

graph{x^2/(x^2-1) [-22.8, 22.81, -11.4, 11.42]}