An asymptote to a curve f (x) is a line that the curve approaches but never meets.

Horizontal Asymptote :

  If  , then  f (x) has  a Horizontal Asymptote y = a.

Vertical Asymptote :

  If , then the line x = b is a Vertical Asymptote.

Oblique Asymptote :

  If ,then the line y = mx + c is an Oblique Asymptote to f (x).

  The following applet helps you to analysis asymptote for rational function .

To Use Applet :

From the drop down menu next to show a function and click on the button "Show Graph".
You can move the sliders for the the movement of the graph and the asymptote.
You can observe as following :