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Function from a table worksheets

An input–output table is a function when every input appears with just one output. These free printable worksheets ask that of a table, where the inputs are already gathered into a row.

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Function from a table
Function from a table worksheet — Input–output tables, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

In a table the inputs sit together along the top, so half the work — collecting them — is already done, and what is left is to check whether any repeats and disagrees. That is why the table is a separate sheet from the ordered-pairs one: it is the same rule read off a different shape, and the easier of the two to scan once a child knows to look only at the input row.

Why this sheet works

Nothing here is sorted. A table whose inputs run 1, 2, 3, 4 would put any duplicate side by side and announce it, so the columns are shuffled and every sheet also carries tables that repeat an OUTPUT while staying a function — a flat run where each different hour reads the same temperature. A repeated output is allowed; only a repeated input with two answers is not.

How this one works

One question from this sheet, worked through a step at a time.

x: 3, 5, 5, 6 y: 9, 32, 44, 2

x3556y932442
x3556y932442inputs3556
x3556y932442inputs3556
Is this a function?No
  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: 3, 5, 5, 6. 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 32 and also to 44, 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.

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