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
 here and/or 
 here
 here for specifics.
Rap