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I am planning to make an application that can graph all functions.(polynomials, rational, trigonometric,etc) but I can't make a decision on which programming language I am going to use. I am choosing between Java and what are the ups and downs of these languages? Which one would be better to use? Thanks!

In my opinion, it doesn't matter which language you choose. The challenges and problems you will face are going to be independent of the implementation language. The major difference between languages as they relate to graphing functions will be in how you draw the graph and show it to the user. Java and VB.NET are different, but for your purposes, they're roughly equivalent.

If you're looking for a Java/VB.NET comparison, I'm sure a quick Internet search will turn up a wide variety of opinions.

I agree with gusano79. What you really need to do here is to come up with rules to obtain 2 end points of each line you are going to display. You could use tangent, maybe?

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