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

Relation A set of ordered pairs. A relations can be represented as In a table x y 3 4 Mapping x y Graph 3 4

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)

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 1 2 If a value is repeated in the range -2 4 or the domain only list it once in 0 5 the mapping. -3

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 1 2 -2 4 0 -3 1 5 In a table you write each value even if it is repeated.

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.

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)

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