InputA value that goes in. Every input sits in the first oval.
OutputA value that comes out. An arrow points to it from its input.
DomainThe set of all the inputs: the whole first oval.
RangeThe set of all the outputs that the arrows point to.
Which kind of mapping 3
One-to-one functionEvery input has its own output, and no two share one.
Many-to-one functionTwo or more inputs share an output. It is still a function, because each input has one arrow.
Not a functionOne input has two outputs, which a function never allows. It is still a relation.
How this list was compiled: Read 2026-10-01. (1) Wikipedia, Function (mathematics), https://en.wikipedia.org/wiki/Function_(mathematics) : a function from set X to set Y pairs each element of X with exactly one element of Y; X is the domain; the image, sometimes called the range, is the set of images of every element of the domain; a function is one-to-one (injective) when different inputs always give different outputs. Injective function, https://en.wikipedia.org/wiki/Injective_function : also known as a one-to-one function; a non-injective function is sometimes named many-to-one. (2) Math is Fun: What is a Function?, https://www.mathsisfun.com/sets/function.html (a function ties each input to an output; it may be many-to-one, never one-to-many; a relationship that breaks the rule is a relationship still, but no function; the set of elements pointed to is the range); Domain, Range and Codomain, https://www.mathsisfun.com/sets/domain-range-codomain.html (the domain is every value that goes into a function, the range all the values that come out); Injective, Surjective and Bijective, https://www.mathsisfun.com/sets/injective-surjective-bijective.html (injective is also called one-to-one: no two inputs point to the same output). Licence: own work
The drawing: Drawn for this site on 2026-10-01 from plain geometry; nothing traced. Licence: own work
How it works
A blank mapping diagram sheet to print: four pairs of empty ovals with lines for the inputs and outputs. Below them are three worked diagrams, a many-to-one function, a one-to-one function and a mapping that is not a function.
Read the full guide
Filling in a blank diagram
Write the inputs in the first oval and the outputs in the second, then draw an arrow from each input to its output. The line above each oval is for its name: domain over the first, range over the second.
Is it a function?
Look at the arrows that leave each input. If every input has exactly one, the mapping is a function. If any input has two, it is not.
Two arrows may end on the same output. Two arrows may never start from the same input.
Questions and answers
What is a mapping diagram?
Two ovals side by side, the inputs in the first and the outputs in the second, with an arrow from each input to the output it goes to.
How do you tell if a mapping diagram is a function?
Check each input. A function gives every input exactly one output, so each number in the first oval has exactly one arrow leaving it.
What are the domain and range on a mapping diagram?
The domain is the set of inputs, the whole first oval. The range is the set of outputs that arrows point to, in the second oval.