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Relationships – or relations – express the ways in which two quantities are related. They can be represented as sets of ordered pairs, tables of values, mapping diagrams, rules, or graphs.

Special types of relations, called functions, are presented as a relation in which each input value corresponds to exactly one output value. There are different ways to determine if a relation is a function depending on the way the relation is represented, including the use of mapping diagrams and the Vertical Line Test.

Function notation, $f(x)=y,$ is introduced to show how one quantity is dependent upon another. Because functions show how two quantities relate, they are useful in analyzing situations in context. Key features of the graphs of functions are used to further describe the behavior of functions.

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