A bmapping/b transforms one set of numbers into another set.

A mapping is a function if every input leads to a distinct output. Functions can be one-to-one or many-to-one mappings. One-to-many mappings are bnot/b functions.
[row][col]pA one-to-one mapping, therefore a function[/p]mtaimg/images/topics/2/2-191-1.png[/mtaimg]/col
[col]pA many-to-one mapping, therefore a function[/p]mtaimg/images/topics/2/2-191-2.png[/mtaimg][/col]/row
[row][col]pA one-to-many mapping, therefore bnot/b a function[/p]mtaimg/images/topics/2/2-191-3.png[/mtaimg]/col
[col]pA many-to-many mapping, therefore bnot/b a function[/p]mtaimg/images/topics/2/2-191-4.png[/mtaimg][/col]/row
uDomain and range/u

The bdomain/b of a mapping is the set of all possible inputs. Graphically, the domain is the set of possible (x) values.

The brange/b of a mapping is the set of all possible outputs. Graphically, the range is the set of possible (y) values.

uNotation/u

(x∈ℝ) means "(x) is in the set of all real numbers"

One-to-one and many-to-one mappings are functions.

One-to-many mappings are not functions.

The bdomain/b of a mapping is the set of all possible inputs. Graphically, the domain is the set of possible (x) values.

The brange/b of a mapping is the set of all possible outputs. Graphically, the range is the set of possible (y) values.

(x∈ℝ) means "(x) is in the set of all real numbers"