What is a function in mathematics?
Answer
A function is a relation that assigns to every element of one set exactly one element of another set.
The working
Definition
A function f from set A to set B, written f: A → B, pairs each element of A with a single element of B. No input can have two outputs.
Domain and range
The set A of all inputs is the domain, and the set of actual outputs is the range, which is a subset of the codomain B.
Notation
If x is an input, its output is written f(x). For example, f(x) = 2x + 1 gives f(3) = 7.
Key test
A relation is a function only if every input maps to exactly one output. Graphically, any vertical line meets the curve at most once.
Example
f(x) = x² is a function since each x gives one value, but a relation where one x gives two y values is not.
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