Input-Output Table — Definition, Formula & Examples
An input-output table is a chart that lists pairs of numbers where each input is changed into an output by following the same rule. It helps you see the pattern a rule creates and predict what output any new input will produce.
An input-output table is a two-column (or two-row) representation of a function in which the first column lists domain values (inputs) and the second column lists the corresponding range values (outputs) produced by applying a consistent rule to each input.
How It Works
One column is labeled "Input" and the other "Output." A rule, such as "multiply by 3 then add 1," is applied to every input to get its output. To find the rule from a completed table, look at what operation connects each input to its output. Once you know the rule, you can fill in missing values or extend the table to new inputs.
Worked Example
Problem: Find the rule for this input-output table and use it to find the output when the input is 10.
| Input | Output |
|-------|--------|
| 1 | 5 |
| 2 | 8 |
| 3 | 11 |
| 4 | 14 |
Look for a pattern: Each time the input goes up by 1, the output goes up by 3. This tells you the rule multiplies the input by 3.
Check with addition: When the input is 1, multiplying by 3 gives 3, but the output is 5. So the rule also adds 2.
Apply the rule to input 10: Substitute 10 into the rule.
Answer: The rule is "multiply by 3, then add 2." When the input is 10, the output is 32.
Why It Matters
Input-output tables are one of the first ways students explore functions before they learn equations or graphing. Understanding them builds a foundation for algebra, where the same idea is written as a formula like .
Common Mistakes
Mistake: Checking the rule against only one row of the table and assuming it works for all rows.
Correction: Always verify your rule against every input-output pair in the table. A rule that fits one pair may not fit the others.