How to find assymptopes and domain easily.

[BigMoosie]

Hi, I am creating a computer program that graphically draws mathematical functions, later I will make it do other curves as well but for now I need to solve something.

 

How it works is by testing 0, then 0.01 and drawing a line between the two etc, sometimes it will jump from a very large number to a very small number when it reaches an assymptope, often the assymtopte is between the two test numbers so it is not detected. In that case a vertical line is drawn on the page. I know how to find assymtoptes myself, usually just by looking for zeros in denominators but the computer doesnt know that.

 

• How would I find these assymptopes?
  
• Is there a simple way of knowing if f(x) and f(y) are part of the same curve?
  
• Less importantly, how could I find assymtoptes other than vertical ones?
  

[Dave]

For a general function, you have to use limits and the like to determine where asympotes will occur. For your program however, I would suggest that the easiest way to detect the asymptote would be to look for the extremely large changes in values (like you get with 1/x). This would be the simplest way, I think

[BigMoosie]

I was considering that but occasionally it might guess incorrectly, but doubtful. I was intending however for it to also find infitessimal gaps like:

 

x(x-1)

------

x - 1

 

My program will draw this as a straight line, but unless the testing values fall directly on 1 then it will miss the tiny hole at (1,1). Is there no way of finding that?

[Dave]

Not that I can think of. Plotting is rather a complex business... perhaps some additional checks that I haven't thought of can be implemented. I'll give it some thought.