Function Tables: Complete Input-Output Rules and Match Tables

Algebra and Function Practice

A function table shows how each input value pairs with exactly one output value. When you are given a rule, apply it to every input to complete the table. When you are given a table, test candidate rules against every pair to find the match. This lesson builds both skills with clear conventions, checkable arithmetic, and a rubric that allows valid alternative representations.

Practice materials: Printable downloads are not available for this lesson yet. Use the instructions and four exercises below.

Reading and Applying a Rule

A rule such as 'multiply by 3, then add 1' tells you the operation order. Write the rule as output = 3 times input plus 1. Apply it to each input in the table, one row at a time, and record the output in the same row.

Keep units consistent. If inputs are in centimetres, outputs are in centimetres unless the rule changes the unit. Label any numerical values you choose as hypothetical examples when measuring real equipment.

1. Copy the rule and identify the operations and their order.
2. For the first input, substitute the value into the rule and compute the output.
3. Record the output beside its input in the same row.
4. Repeat for every input, checking each calculation once.
5. Look for a pattern in the outputs to catch a likely error.

Matching a Table to a Rule

To match a table to a rule, test each candidate rule on at least two input-output pairs. A rule must work for every pair in the table, not just one. If a rule fails on any pair, eliminate it.

When two rules both fit the given pairs, look for a pair that distinguishes them, or state that the table is consistent with both rules for the shown inputs. Matching is about consistency with the displayed data.

1. List the candidate rules.
2. Choose two pairs from the table and compute each rule's output for those inputs.
3. Eliminate any rule that does not produce the table's output for both pairs.
4. Test remaining rules on a third pair if available.
5. State the matching rule and show one verification calculation.

Convention for Handwritten Tables and Diagrams

Use a two-column table with 'input' on the left and 'output' on the right. Write one pair per row. For any diagram, use a horizontal baseline and a midline; x-height is measured from baseline to midline. Letter styles vary, so accept any legible style that keeps x-height within the stated band.

This convention allows valid alternatives: a table may be drawn vertically or horizontally as long as each input is paired with its output, and a diagram may use different letter shapes provided the baseline-to-midline x-height is respected.

1. Draw the table with clear column headings.
2. Write each input once and its output in the same row.
3. For diagrams, mark baseline and midline lightly.
4. Keep lowercase letters' x-height between baseline and midline.
5. Label any measured values and note that chosen numbers are hypothetical examples.

Worked example

Rule: output = 2 times input plus 5. Complete the table for inputs 0, 1, 3, and 4. Then verify one row.

Four practice exercises

Common mistakes

• Applying operations in the wrong order, such as adding before multiplying when the rule says multiply then add. Rewrite the rule with parentheses or a sequence: output = (3 times input) + 1. Compute the multiplication first.
• Testing a candidate rule on only one pair and declaring a match. Test every pair in the table, or at least three pairs, and eliminate any rule that fails on one pair.
• Mixing units or dropping labels when the rule changes the unit. Write the unit beside each column heading and convert before computing if needed.
• Assuming a single universal handwriting style is required for diagrams. Follow the baseline-to-midline x-height convention and accept any legible letter style within that band.

Self-check rubric

• Correctly applies the operation order in the rule for every input.
• Records each output in the same row as its input.
• Tests candidate rules against every displayed pair when matching.
• Shows at least one verification calculation.
• Uses consistent units and labels columns.
• For diagrams, keeps x-height between baseline and midline and accepts any legible letter style within that band.

Questions and answers