Function or Not a Function

What to decide

A relation is a function if each input has exactly one output. If one input is paired with two different outputs, it is not a function.

How to check

1. Look at each input value.
2. See whether it appears with more than one output.
3. If every input is matched to only one output, the relation is a function.
4. If any input repeats with different outputs, the relation is not a function.

Useful checks by representation

• Table or list: compare repeated inputs carefully.
• Ordered pairs: watch for the same first coordinate appearing with different second coordinates.
• Graph: use the vertical line test; if a vertical line hits the graph more than once, it is not a function.

Final step

After deciding function or not, write the answer clearly and simplify any expression if the problem asks for one.

Quick verification

Ask: “Does every input produce only one output?” If yes, it is a function. If no, it is not a function.