Definition: A function is a rule that assigns exactly one output to each input, so no input ever gives two different outputs.
What is a function?
A function pairs every input with exactly one output. Think of a vending machine: press B4 and you always get the same snack.
How can you show one?
With an equation, table, graph, or mapping. The rule y = 3x – 2 turns input 4 into 10.
How do you test it?
On a table or list of pairs, check that no x-value repeats with different y-values. The pairs (1, 5), (2, 7), (3, 5) are a function, since two inputs may share an output. The pairs (1, 5), (1, 8) are not.
On a graph, use the vertical line test: if any vertical line meets the graph twice, it is not a function.
What are the terms?
The input is the independent variable and the set of inputs is the domain. The output is the dependent variable and the set of outputs is the range.
What is a common mistake?
Thinking two inputs cannot share an output. That is allowed. What is forbidden is one input with two outputs.