Suppose $f$ is a real valued function with domain a subset of
real numbers, $D$.
Definition: A mapping diagram for $f$ is
a figure consisting of two parallel number lines (or axes) and a set
Points on one (source or input) line represent numbers
from the domain, the source (controlling or independent) variable
Points on the other (target or output) line represent
numbers from the co-domain, the target (controlled or dependent)
An arrow in the diagram has its tail on a point representing a
selected number, $a$, on the source (domain) line.
The head of the arrow points to the function value,
$f(a)$, for the number $a$, represented by a point on the
target (co-domain) line.
Other Names: Mapping diagrams are also described as function diagrams, arrow diagrams, dynagraphs, parallel coordinate graphs, or cographs. They have also been connected in discussions to nomograms.
Conventions: When the axes are displayed
vertically, the axis on the left represents the source
line ( "the X axis") and the axis on the right represents the
target line ("the Y axis").
Both lines are oriented with the larger numbers higher on the
When the axes are displayed horizontally, the axis on the
top represents the source line ( "the X axis") and the axis on
the bottom represents the target line( "the Y axis").
Both lines are oriented with the larger numbers further to the
right. In some uses the representation is reversed with the
bottom line representing the source and the top line representing the
In this resource, mapping diagrams will be displayed