The Definition of a Function

Function: Let A and B be two nonempty sets. A function from A to B is a rule of correspondence that assigns to each element in A exactly one element in B.

A function is like a machine where A represents the set of inputs, which are inserted into the function to determine each output. Each resulting output is part of the set B.

FUNCTION

The set A in the above diagram represents the domain, i.e. the set of all possible inputs. The letter used to represent the elements of a functions domain is the independent variable.

The set B in the above diagram represents the range, i.e. the set of all outputs, which result from the given inputs. The letter used to represent the elements of the functions range is the dependent variable.

Note: One way to determine the range of a function is to solve the equation for y.

Function Notation:

If , then ,

,

.

If , then .