A function takes an input and gives exactly one output. Think of a vending machine: press B4, get one specific item. Press it again, get the same item. The input is the button; the output is the snack.

Functions are written as f(x), read "f of x." The set of allowed inputs is the domain; the set of possible outputs is the range. A function can be defined by a formula, a graph, a table, or a rule. The key requirement is that each input has only one output.

Functions model relationships throughout science and engineering. Linear functions describe constant rates; exponential functions describe growth and decay; trigonometric functions describe waves. Calculus studies how functions change. The concept is central to modern mathematics.

• Each input maps to exactly one output
• Written as f(x)
• Domain and range describe inputs and outputs
• Models relationships in science and engineering