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 Uses

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What is Being Visualized

• Input and output
• Function

Visualization Techniques

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")