is a in which each is assigned to exactly one
. The of all possible inputs is called the of the function and the set of all possible outputs is called the . If x
represents the inputs and y
the outputs of a function, it is often said that
y is a function of x
y depends on x.
This way of representing the is called . A function can be represented using a , a , an , or a graph.
Note that every
function is a relation, but not every relation is a function. In the following applet, three different relations are analyzed to determine whether they are functions.
In Relation III, although one of the outputs corresponds to two different inputs, it is still a function because each input has exactly one output. Depending on how a relation is represented, there are different methods to determine whether or not it is a function.
| Determining Whether a Relation Is a Function
| If represented as
| A set of or a table of values
|| A mapping diagram
| A graph in the