In Algebra, a function is a fundamental concept that describes a special relationship between inputs and outputs. Think of a function as a machine: you put an input value in, and the machine follows a specific rule to produce exactly one output value. For example, if we have the function f of x equals x squared, and we input 3, the machine will always output 9. The key characteristic is that each input produces only one unique output.
Function notation uses the symbol f of x to represent a function. The letter f is the function name, and x represents the input variable. For example, if we have f of x equals 2x plus 1, this tells us the rule: multiply the input by 2 and add 1. When x equals 1, f of 1 equals 3. When x equals 2, f of 2 equals 5. This notation makes it clear what the input is and what the corresponding output will be.