Conic sections are a start--circle, ellipse, hyperbola, hyperbola. Then there are the trigonometric functions, sine, cosine, tangent, and inverses. How about logarithmic and exponential functions.
As for me I'd consider this definition for generalities
Quote:In mathematics, a function is a relation, such that each element of a set (the domain) is associated with a unique element of another (possibly the same) set (the codomain, not to be confused with the range). The concept of a function is fundamental to virtually every branch of mathematics and every quantitative science.
en.wikipedia.org/wiki/Mathematical_Function
and look
here and/or
here for specifics.
Rap