Function Basics

A function is a rule that pairs each input with exactly one output. That single idea drives everything else — the vertical-line test, domain and range, and how we compare one function to another.

• Is it a function? Each input may appear only once. On a graph, a vertical line may cross at most once (the vertical-line test).
• Domain and range are the sets of allowed inputs and the outputs they produce — and in a real-world problem, the practical domain is only the inputs that make sense (you can't have $-3$ people).
• Comparing functions means lining up two functions given in different forms — a table, a graph, an equation, a description — and reading the same feature from each.

These are real, released Regents questions.