Graphic Representation
Introduction
A graphical representation is a graphic or topological representation of a mathematical or conceptual structure of a certain complexity. In a graphic representation, each entity of the structure is assigned a geometric object (point, node, arrow, ...) and the relationships between objects are presented through geometric distances, arrows or other graphic entities.
Examples
Graph of a function
- An ordinary mathematical function
f
:
A
→
b
{\displaystyle f:A\to B}
!{\displaystyle f:A\to B} where
A
,
b
⊂
R
{\displaystyle A,B\subset \mathbb {R} }
!{\displaystyle A,B\subset \mathbb {R} }, formally it is a subset
g
f
⊂
A
×
b
{\displaystyle G_{f}\subset A\times B}
!{\displaystyle G_{f}\subset A\times B} that meets these specifications:.
That is, for every element
to
∈
A
{\displaystyle a\in A}
!{\displaystyle a\in A} there exists a single element such that
(
to
,
b
)
∈
g
f
{\displaystyle (a,b)\in G_{f}}
!{\displaystyle (a,b)\in G_{f}} or in more conventional notation
b
=
f
(
to
)
{\displaystyle b=f(a)}
!{\displaystyle b=f(a)}. The subset
g
f
⊂
A
×
b
{\displaystyle G_{f}\subset A\times B}
!{\displaystyle G_{f}\subset A\times B} is called the "graph" of the function and can be represented in the plane as the graph of a function.