When we think of a function as a mathematical model, or as a piece of a larger mathematical model, the representation we choose may determine the way in which we go about solving the mathematical problems within the model. In general, we solve problems involving algebraic, graphical, and numerical representations of functions with quite different methods.

If a function can be given more than one representation, we may be able to investigate its behavior using several different methods. An important part of the mathematical deduction would then involve a comparison of the results from the different methods.