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Example: Determining Whether Ordered Pairs Represent a One-to-One Function

Consider two sets of ordered pairs to determine if each is a function and, if so, whether it is one-to-one.

ⓐ The set {(3,27),(2,8),(1,1),(0,0),(1,1),(2,8),(3,27)}\{(-3, 27), (-2, 8), (-1, 1), (0, 0), (1, 1), (2, 8), (3, 27)\}: Each xx-value is paired with only one yy-value, so the relation is a function. However, examining the yy-values reveals repetitions — for instance, the pairs (3,27)(-3, 27) and (3,27)(3, 27) share the same yy-value of 2727, and the pairs (1,1)(-1, 1) and (1,1)(1, 1) share the yy-value of 11. Because not every yy-value corresponds to a unique xx-value, this function is not one-to-one.

ⓑ The set {(0,0),(1,1),(4,2),(9,3),(16,4)}\{(0, 0), (1, 1), (4, 2), (9, 3), (16, 4)\}: Each xx-value maps to exactly one yy-value, confirming it is a function. Additionally, each yy-value — 00, 11, 22, 33, and 44 — appears only once, meaning every yy-value is paired with a unique xx-value. Therefore, this function is one-to-one.

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Updated 2026-05-25

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