Definition of a Function
At it's most basic, a function is a set from one set of numbers, called the domain, to another, called the codomain.
It returns a single, unique number for every number that it operates on. That is, the function may send more than one value of(from the domain) to the same value of(in the codomain), but may not send any single value ofto more than one value of
a, b, c, e, g and h are functions.
d and f are not.
Note that it is not necessary that some value ofexists for eachnor that the graph join up. The points of h do not join up because the graph jumps at certain points, but h still illustrates a function.
An easy test is that if a vertical line is drawn through any point of theplane, the graph defines a function if the line intersects the graph at most once.