A
function 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
or that
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
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If represented as
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Use
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a set of or a table of values
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a mapping diagram
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a graph in the
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the
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