how to determine a function of a specific shape I have become very passionate about mathematics lately, but one question is really irritating me,
HOW do you determine a function for ANY specific shape ?
Is there a certain procedure that enables me to get a function out of a random shape or curve ?
I use this a lot in machine learning but all i do is apply some functions and formulas made by some mathematician and i really would like to know if initially i could get to at least have a vague idea of how a function would look like or even how a shape would be if written in a function
 A: Begin to pay close attention when applying "some functions and formulas" to see how each function corresponds to its respective graph, and look for patterns, or prototypes. This will help you begin to develop better intuition when you see a graph, since you'll already have encountered and noted, something resembling it. 
What is the prototypical shape of a quadratic polynomial? A cubic? 
Know your conic sections! (And learn why they are called conic sections!): The circle, ellipse, hyperbola...How does each vary depending on their parameters.
What about the important exponential functions, and how they vary depending on parameters? 
Which leads us to logarithmic functions...
And trigonometric functions...
Start attempting to classify shapes into any of the above categories, and if a shape or curve doesn't fit any of the above, consider compositions of functions, etc. You might also want to understand even vs. odd functions, axes of symmetry, etc.
There's no quick and clever way to acquire this intuition without beginning to pay attention, ask questions, create schemes, making guesses, etc. 
