Question

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

Answer 1

A relation is a set of numbers that have a relationship through the use of a domain and a range, while a function is a relation that has a specific set of numbers that causes there to be only be one range of numbers for each domain of numbers. All functions are relations, but all relations are not functions.

Answer 2

Given two sets $A$ and $B$, the "starting" set is called the domain, while the "landing" set is called the codomain.

With that being said, a relation is any way you can associate any number of elements in the domain with every number of elements in the codomain.

A function has more restriction: you can associate one and only one output for every input.

If you visualize this with arrows linking domain and codomain, in order for a relation to be a function, only one arrow can start from each point in the domain.

The domain is thus the set of elements from whence an arrow starts. The range is the subset of the codomain, given by the elements that are reached by at least one arrow.