You probably need to post some code and provide an example of a run of the program, even though you haven't written the program yet. You need to decide what kind of functions are legal (polynomials, exponents, logarithms, etc.). Have the user enter the function, read it in as a string, then parse the string in such a way that you can tell what kind of function it is (e.g. polynomial, whether it's a legal function that you can handle, then parse the string further to extract the relevant numbers (i.e. coefficients and exponents in a polynomial). But I think you'll have to read the function in as a string from the user.

The big thing is to decide what input your program needs to be able to handle, what assumptions it can make as far as good input, then go from there, in my opinion.