A function is a rule or a relation that assigns to each input exactly one unique output. In mathematics, a function takes an input value from a set called the domain and produces an output value in another set called the codomain. The input is often called the independent variable or argument, and the output is called the dependent variable.
Key Characteristics of a Function
- It maps each input value to exactly one output value.
- The input values come from the domain.
- The output values belong to the codomain or range.
- The rule or mapping can be expressed as an equation, a set of ordered pairs, a graph, or a verbal description.
For example, a function fff that adds 3 to a number xxx is written as f(x)=x+3f(x)=x+3f(x)=x+3. If the input is 2, the output is 5; if the input is 8, the output is 11, and so forth. A function can be thought of like a machine: it takes an input, processes it according to a defined rule, and produces an output. The crucial point is that each input must relate to one and only one output for the relation to qualify as a function. This foundational idea is used to describe relationships in algebra, calculus, and many applied fields.
