Function Machines — Input & Output Rules (Grades 5–6)
A function machine takes an input number, applies a rule, and gives an output — like a rule "multiply by 3, then add 1." Put in 2, get out 7. The same rule always gives the same output for a given input. Reading a table of inputs and outputs, you can work out the hidden rule by asking "what was done to every input to get its output?"
Understanding function machines — input/output rules
A function machine takes an input number, applies a rule, and gives an output — like a rule "multiply by 3, then add 1." Put in 2, get out 7. The same rule always gives the same output for a given input. Reading a table of inputs and outputs, you can work out the hidden rule by asking "what was done to every input to get its output?"
Key Idea
A function machine takes an input number, applies a rule, and gives an output — like a rule "multiply by 3, then add 1." Put in 2, get out 7. The same rule always gives the same output for a given input. Reading a table of inputs and outputs, you can work out the hidden rule by asking "what was done to every input to get its output?"
Seeing it in action
Worked example
A machine uses a steady "multiply then add" rule. It turns 2→7, 3→10, and 4→13. What is the rule, and what does 5 give?
Each output is input ×3 + 1 (2·3+1 = 7, 3·3+1 = 10, 4·3+1 = 13 — all three confirm it).
So 5 gives 5·3 + 1 = 16.
Apply ×3 + 1 to move from input to output.
Try a few
Rule "×2": input 6
Rule "+4": input 9
A "multiply then add" machine gives 1
5, 2
Function Foundry
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