Here's a breakdown:

* Input: The value you put into the function.

* Output: The value the function produces based on the input.

* Domain: The set of all possible inputs.

* Codomain: The set of all possible outputs.

* Uniqueness: Each input has only one corresponding output.

Formal Definition:

A function f from a set X to a set Y, denoted f: X → Y, is a rule that assigns to each element x in X a unique element f(x) in Y.

Example:

The function f(x) = x² takes an input (x) and squares it.

* Domain: All real numbers

* Codomain: All non-negative real numbers

* Example: f(3) = 9, f(-2) = 4

Key Points:

* Functions can be represented in different ways: formulas, graphs, tables, etc.

* The uniqueness property distinguishes functions from other relations, where an input can have multiple outputs.

Let me know if you'd like more examples or explanations!