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Function from a table, step by step

An input–output table is a function when every input appears with just one output.

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The question
x19558y2033456

Is this a function?

x: 19, 5, 5, 8 y: 20, 3, 34, 56

x19558y2033456
x19558y2033456inputs19558
x19558y2033456inputs19558
5 → 3 and 5 → 34
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 top row of the table.
  2. Pull the inputs out on their own and look at them together: 19, 5, 5, 8. Nothing about the outputs matters yet.
  3. 5 is in that list twice, and the two pairs it belongs to do not agree: the input 5 goes to 3 and also to 34, 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 top row of the table.

  2. 02

    Pull the inputs out on their own and look at them together: 19, 5, 5, 8. Nothing about the outputs matters yet.

  3. 03

    5 is in that list twice, and the two pairs it belongs to do not agree: the input 5 goes to 3 and also to 34, 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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