How to identify if generic function can be created??

Methodology for the generic function in software engineering??

Hi,

I would like to inquire your guidance on sotfware methodolody.
I took one software engineering class a while back and I don't know how I need to go about identifying a methodoloy in software development.(not sure if I am using the proper terminology to describe my question!!)
This is what I am trying to find out.
Is there some kind of methodoloy I can use and apply in order to develop a generic function(method) to do certain things with several different inputs??
I have developed several applications with different functionalities for different customers.
Each time I get a new customer, I had to develop from the scratch.
I am trying to develop a baseline flatform with  generic functions which can handle very basic functions.
Say I have three different functions from three different applications but the main job of those function is same.
How can I identity if I can create a generic funtion from those different applications?

What things do I need to analyze and identify if the generic function can be created??
I am sorry if I am not explaining correctly but I hope I can get a kick start from you.
Thanks much.