**Function machine** is a popular metaphor for visualizing input and output of a procedure, or the idea of a function, and related notions. It is accessible to toddlers, yet is robust enough to be taken to college-level work.

## History and Known UsesEdit

...

## What is Being VisualizedEdit

- Input and output
- Function

## Visualization TechniquesEdit

The basic visual metaphor is a machine that "does something" to objects that enter into one of its openings, and exit through another. In this form, it immediately supports:

- Input and output
- Inverse functions ("machine working backwards")
- Domain and range ("what can go into the machine and what can come out")

Extensions of the metaphor include:

- Iteration and cycles("a tube connecting the output of the machine to the input")
- Multi-variable functions ("many input openings")
- Composition of functions ("two or more machines attached together")