Is {(1, 2); (2, 3); (3, 4); (2, 5)} a function?

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Is {(1, 2); (2, 3); (3, 4); (2, 5)} a function?

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Answer 1 · 2015-07-04T03:29:22

No it is not a function.

Explanation:

A function is a relation (a set of ordered pairs) with the additional property that: no two pairs have the same first element and different second elements.

The definition is often stated as: A relation in which every $x$ value is associated with exactly one $y$ value. "Exactly one means one but two or more:

${(1, 2); (2, 3); (3, 4); (2, 5)}$ includes the points $(2,3)$ and $(2,5)$ . Therefore this set of pairse is not a function.

Note

${(0,1), (1,3), (2, 5), (3, 5)}$ is a function.
(It is ok to have different first elements and the same second elements. The definition of function is very precise.)

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Is {(1, 2); (2, 3); (3, 4); (2, 5)} a function?

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