Example

Example: Sets of Ordered Pairs Not Representing a Mathematical Function

Consider the relation given by the set of ordered pairs: {(9,3),(4,2),(1,1),(0,0),(1,1),(4,2),(9,3)}\{(9, -3), (4, -2), (1, -1), (0, 0), (1, 1), (4, 2), (9, 3)\}. To determine if this relation is a mathematical function, we inspect the coordinates. The xx-value 99 is matched with two different yy-values (3-3 and 33), and the xx-value 44 is matched with two different yy-values (2-2 and 22). Because an xx-value corresponds to more than one yy-value, this relation is not a function. The domain is {0,1,4,9}\{0, 1, 4, 9\} and the range is {3,2,1,0,1,2,3}\{-3, -2, -1, 0, 1, 2, 3\}.

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Updated 2026-05-06

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