Function
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
A function is a special type of relationship between two sets of numbers or objects. Specifically, a function is a rule or correspondence that assigns each element from one set, called the domain, to exactly one element in another set, called the range.
Here's a more formal definition:
Function: A function f from a set A to a set B is a rule that assigns to each element x in A exactly one element f(x) in B. The set A is known as the domain of the function, and B is the range.
For example, if f is a function that assigns each person to their age, then each person (an element in the domain) has exactly one age (an element in the range).
In graphical terms, if you plot the function on a coordinate plane, each x-value (input) corresponds to exactly one y-value (output). This can be visually checked using the Vertical Line Test: if any vertical line crosses the graph of the function at more than one point, then the graph does not represent a function.