Transformations - Spatial Mathematics: Theory and Practice through Mapping - page 57

Relation

Function

x y x y

x 1 x 1

x 2 y x 2 y

x 3 x 3

y 1
y 2
y 3

x

Figure 3.1 A function requires that each element of X be associated with only one
element of Y (although many different elements of X may be associated with the
same element of Y). A relation removes this restriction, allowing one element of X
to be associated with many elements of Y. Thus, every function is a relation, but
not every relation is a function. Based on Arlinghaus, S. L. and W. C. Arlinghaus.
2001. The Neglected Relation. Solstice: An Electronic Journal of Geography and
Mathematics. Vol. XII, No. 1. Ann Arbor: Institute of Mathematical Geography.
http://www-personal.umich.edu/%7Ecopyrght/image/solstice/sum01/compplets.
html.

Figure 3.2 (a) One-to-one function. (b) Many-to-one function. Many x-values (black
dots) correspond to one y-value (height of horizontal line). (c) One-to-many rela-
tion. One x-value corresponds to many y-values (black dots). Based on Arlinghaus,
S. L. and W. C. Arlinghaus. 2001. The Neglected Relation. Solstice: An Electronic
Journal of Geography and Mathematics. Vol. XII, No. 1. Ann Arbor: Institute of
Mathematical Geography. http://www-personal.umich.edu/%7Ecopyrght/image/

solstice/sum01/compplets.html