Skill: Determine the rule in an input-output table

An input-output table shows how a rule changes each input into an output. The same rule must work for every row.

Consider this table:

Input	Output
2	6
4	12
6	18

Step 1: Compare one input and its output.

For the first row:

$$2 \times 3 = 6$$

So, multiplying by $3$ might be the rule.

Step 2: Test the rule on the other rows.

$$4 \times 3 = 12$$ $$6 \times 3 = 18$$

The rule works for every pair.

Step 3: State the rule.

The rule is:

Multiply the input by $3$ to get the output.

Do not only look at how the outputs change. The outputs go up by $6$, but the inputs go up by $2$. The important question is: What same operation changes each input into its output?