A function approximation problem asks us to select a function among a well-defined class that closely matches (approximates) a target function.
There are two major classes of function approximation problems. For known target functions approximation theory investigates how certain known functions can be approximated by a specific class of functions (for example, polynomials or rational functions).
In the second class of problems, the target function (say f) may be unknown. Instead of an explicit formula, only a set of points of the form (x, f(x)) is provided. Several techniques for approximating f may be applicable (depending on the structure of the domain and codomain of f), such as interpolation, extrapolation, regression analysis, and curve fitting.