Treat an expression as an input-output rule

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Treat an expression as an input-output rule

A function assigns one output to each permitted input. The rule 2x+3 first doubles the input, then adds 3. A table records individual input-output pairs, while the expression describes the same process for every input in the domain.

Different inputs can sometimes share an output. The squaring function gives 9 from both 3 and −3. This does not stop it being a function: each individual input still has exactly one output. It does matter when trying to reverse the rule.

Use a function machine to keep the order of operations visible. Multiplying then adding is usually different from adding then multiplying. The domain and output meaning should be stated when a rule models a real quantity.

Worked example: Apply the rule 2x+3 to input 4.

Double 4 to obtain 8.

Add 3.

Answer: 11.

Check your understanding: Does x² give one output for input−3?

Answer: Yes: 9.

Why: A function permits different inputs with the same output, but not two different outputs for a single permitted input.