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Function from ordered pairs, step by step

A set of ordered pairs is a function when no input turns up twice with different outputs.

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The question

Is this a function?

(14, 34) (8, 5) (14, 6) (9, 12)

pairs(14, 34)(8, 5)(14, 6)(9, 12)
pairs(14, 34)(8, 5)(14, 6)(9, 12)inputs148149
pairs(14, 34)(8, 5)(14, 6)(9, 12)inputs148149
14 → 34 and 14 → 6
Not a function
  1. A function has one rule: every input gets exactly ONE output. So there is only one column to check — the inputs, which are the first number in each pair.
  2. Pull the inputs out on their own and look at them together: 14, 8, 14, 9. Nothing about the outputs matters yet.
  3. 14 is in that list twice, and the two pairs it belongs to do not agree: the input 14 goes to 34 and also to 6, and one input may only go to one place.
  4. One input, two different outputs. That is the one thing a function is not allowed to do, so this relation is not a function.

How it works.

  1. 01

    A function has one rule: every input gets exactly ONE output. So there is only one column to check — the inputs, which are the first number in each pair.

  2. 02

    Pull the inputs out on their own and look at them together: 14, 8, 14, 9. Nothing about the outputs matters yet.

  3. 03

    14 is in that list twice, and the two pairs it belongs to do not agree: the input 14 goes to 34 and also to 6, and one input may only go to one place.

  4. 04

    One input, two different outputs. That is the one thing a function is not allowed to do, so this relation is not a function.

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