Pronunciation: /doʊˈmeɪn/ ?

Graph showing the domain as the horizontal axis and the range as the vertical axis.
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 y = 3x - 2, the domain of definition is (-infinity,infinity) or unrestricted, meaning it can take on any value. However, given the real function y = square root of x, the domain of definition is [0,infinity) or x >= 0, 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 f(x)=x^2 with the restriction x >= 0. While negative numbers are defined for the function, they are not in the domain.


  1. domain. WordNet. Princeton University. (Accessed: 2011-01-08).
  2. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry, pp 53-54. International Textbook Company, January 1963. (Accessed: 2010-01-12).
  3. Goldrei, D.C.. Classic Set Theory: For Guided Independent Study, pg 4. Chapman & Hall Mathematics, July 1, 1996.
  4. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra, 6th edition, pp 13-14. Thomson, Brooks/Cole, 2005.

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Domain. 2010-01-24. All Math Words Encyclopedia. Life is a Story Problem LLC.


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Revision History

2010-01-24: Added "References" and "Amazon Resources" (McAdams, David.)
2008-12-30: Added sentence on domain as the input values of a function (McAdams, David.)
2008-12-16: Changed equations to images. Added references to domain of definition, natural domain, and restricted domain. Added 'More Information' (McAdams, David.)
2008-07-11: Added figure 1 (McAdams, David.)
2008-02-04: Corrected typographical error (McAdams, David.)
2007-07-12: Initial version (McAdams, David.)

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