A rational function is the ratio of two polynomial functions. If P(x) and Q(x) are polynomials, then a function of the form R(x) = P(x)/Q(x) is a rational funcation where Q(x) not equal to zero. The domain R(x) is the intersection of the domain of P(x) and Q(x).

 

How is this done, can someone elaborate on the idea of graphing rational functions?i also read that under certain conditions, like Q(x)=0 and P(x)!=0, etc, the graphs formed are Vertical Asymptotes or Horizontal Asymptotes. I could not understand them.

How is this done,

I didn't really notice a question before this point, so could you please clarify what you would like explained in more detail?

can someone elaborate on the idea of graphing rational functions?

Without using tools developed in Calculus, it is rather difficult to get anything more than a vague idea of what a rational function looks like without graphing it on a calculator or computer. A brief description of a Calculus based approach is located in the following thread: rational functions.

i also read that under certain conditions, like Q(x)=0 and P(x)!=0, etc, the graphs formed are Vertical Asymptotes or Horizontal Asymptotes. I could not understand them.

A site with decent introductory material, and a few worked out examples is located here :http://www.scienceforums.net/forums/showthread.php?t=6296.

Using onlt basic differential calculus you can easily graph most such functions by hand. Curve tracing is one the most interesting aspects of calculus as per me.

 

And, yes such functions often give you vertical and horizontal assymptotes, that you can determine using some concepts of limits.

Curve sketching also stands you in good stead when you come to sketch 3D surfaces/paths