Explain the difference between function and relation and the relationship between the domain and the range of a function.

Given two sets X and Y, a relation between X and Y freely associates elements of X with elements of Y, with no restrictions.

A function is a relation with some restrictions: there must be exactly one element of Y connected with each element of X.

The set X is called the domain of the function, and it represents all the possible inputs that we can feed the function with. As we just said, every element of the domain must have a correlated element in Y.

The set Y is called the range of the function, and it represents all the possible outputs that the function can return.

The difference between function and relation is ::

Function: Each input is paired with exactly one output value.

Relation: Describes a relationship and pairs input values with output values.

The relationship between domain and range is ::

Domain: Is an input value. (X value on a graph).

Range: Is an output value. (Y value on a graph).

-Maddy