Input and Output – The Function Machine Idea
A function machine is a simple way to picture how a rule works: you feed in an input value, the machine applies a fixed rule (like “multiply by 3, then add 2”), and an output value comes out. Every linear relationship can be thought of as a function machine with a consistent rule – the same rule applied to every input, producing a predictable output every time.
Just as usefully, function machines can run in reverse: if you know the output and the rule, you can work backwards through the machine's operations (in reverse order, using inverse operations) to find the original input.
Running a Function Machine Forwards and Backwards
To find an output, apply the rule's operations to the input in order. To find an input from a known output, undo the operations in reverse order.
5 × 4 = 20, then 20 + 3 = 23.
Working backwards: 23 − 3 = 20, then 20 ÷ 4 = 5.
Real-Life Application
- Vending machines: insert money (input), receive a snack (output) based on a fixed price rule.
- Currency conversion: an exchange rate is a rule turning one currency (input) into another (output).
- Recipes: scaling ingredient amounts up or down follows a consistent input-output rule.
Key Takeaways
- A function machine applies a fixed rule to turn an input into an output.
- The same rule always produces the same output for the same input.
- Working backwards from an output requires undoing the operations in reverse order.
Practice: Input and Output
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