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4-3 Relations Objective: Students will represent relations as sets of ordered pairs, tables, mappings, and graphs. Students will find the inverse of a relation. S. Calahan 2008

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**Relation A set of ordered pairs. A relations can be represented as**

In a table x y 3 4 Mapping x y Graph

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Domain and Range The domain is the set of the first numbers of the ordered pairs in a relation. (the x value) The range is the set of the second number of the ordered pairs in a relations. (the y value)

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**Mapping Given the ordered pairs express the relation as a mapping.**

A mapping illustrates how each element of the domain is paired with an element in the range. Given the ordered pairs express the relation as a mapping. (1, 2), (-2, 4), (0, -3), (1, 5) x y If a value is repeated in the range or the domain only list it once in the mapping. -3

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**Tables (1, 2), (-2, 4), (0, -3), (1, 5) x y 1 2 -2 4 0 -3 1 5**

Express the relation as a table. (1, 2), (-2, 4), (0, -3), (1, 5) x y In a table you write each value even if it is repeated.

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**Determine the domain and range**

(1, 2), (-2, 4), (0, -3), (1, 5) The domain for this relation is {1, -2, 0}. The range for this relation is {2, 4, -3, 5}. If a value is repeated list it only once.

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Inverse Relations The inverse of any relation is obtained by switching the coordinates in each ordered pair. In a relation (a, b) the inverse is (b, a)

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**Inverse Relation (1, 2), (-2, 4), (0, -3), (1, 5)**

Express the inverse relation (2, 1), (4, -2), (-3, 0), (5, 1)

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