Pronunciation: /reɪndʒ/ ?
Graph showing the domain as the horizontal axis and the range as the vertical axis.
Figure 1: Domain and range.

The range of a function is all values that the dependent variable of the function can take. This also means that the range of a function is all the output values of the function.

In the function y=3x-2, the range is unrestricted, meaning it can take on any value. However, for real numbers, in the function y=square root(x), the range is y>=0, since the square root function returns only non-negative numbers.


  1. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry, pp 53-54. International Textbook Company, January 1963. (Accessed: 2010-01-12). http://www.archive.org/stream/algebraandtrigon033520mbp#page/n70/mode/1up/search/range.
  2. Goldrei, D.C.. Classic Set Theory: For Guided Independent Study, pg 5. Chapman & Hall Mathematics, July 1, 1996.
  3. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra, 6th edition, pp 13-14. Thomson, Brooks/Cole, 2005.
  4. range. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=range&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.

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Cite this article as:

Range. 2008-12-31. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/r/range.html.


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Revision History

2008-12-31: Changed equations from HTML to images. Corrected example range from y>0 to y>=0 (McAdams, David.)
2008-12-23: Added figure 1 (McAdams, David.)
2008-09-04: Added 'More Information' (McAdams, David.)
2008-04-22: Added reference to range of a function (McAdams, David.)
2008-02-27: Converted javascript vocabulary hot links to html (McAdams, David.)
2007-07-12: Initial version (McAdams, David.)

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