Domain
Pronunciation: /doʊˈmeɪn/ Explain

Figure 1: Domain and range.


The domain of a
function
is all values that an
independent variable
can take. The domain of a function is all the
input
values of the function. If the
domain of a function is not explicitly restricted, its domain is called the
domain of definition, all points for which the function is defined.
The domain of definition can also be called the natural domain.
On a Cartesian graph, the domain is typically the
horizontal axis.
In the function , the domain
of definition is
or unrestricted, meaning it can take on any value. However, given the real function
,
the domain of definition is or
, since the square root of a negative
number is
undefined
for the set of
real numbers.
A function can also have a restricted domain. For example,
take the function with the
restriction . While negative numbers
are defined for the function, they are not in the domain.
A subdomain is part of the domain of a funtion.
For example, a subdomain can be
0 ≤ x < 5.

References
 McAdams, David E.. All Math Words Dictionary, domain. 2nd Classroom edition 201501084799968. pg 66. Life is a Story Problem LLC. January 8, 2015. Buy the book
 Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pp 5354. www.archive.org. International Textbook Company. January 1963. Last Accessed 7/3/2018. http://www.archive.org/stream/algebraandtrigon033520mbp#page/n70/mode/1up/search/domain. Buy the book
 Goldrei, D.C.. Classic Set Theory: For Guided Independent Study. pg 4. Chapman & Hall Mathematics. July 1 1996. Last Accessed 7/3/2018. Buy the book
 Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pp 1314. Thomson, Brooks/Cole. 2005. Last Accessed 7/3/2018. Buy the book
Cite this article as:
McAdams, David E. Domain. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/d/domain.html.
Image Credits
Revision History
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
12/4/2018: Added definition of subdomain. (
McAdams, David E.)
7/4/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (
McAdams, David E.)
1/24/2010: Added "References" and "Amazon Resources". (
McAdams, David E.)
12/30/2008: Added sentence on domain as the input values of a function. (
McAdams, David E.)
12/16/2008: Changed equations to images. Added references to domain of definition, natural domain, and restricted domain. Added 'More Information' (
McAdams, David E.)
7/11/2008: Added figure 1. (
McAdams, David E.)
2/4/2008: Corrected typographical error. (
McAdams, David E.)
7/12/2007: Initial version. (
McAdams, David E.)