Pronunciation: /reɪndʒ/ Explain
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. McAdams, David E.. All Math Words Dictionary, range. 2nd Classroom edition 20150108-4799968. pg 150. Life is a Story Problem LLC. January 8, 2015. Buy the book
  2. Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pp 53-54. www.archive.org. International Textbook Company. January 1963. Last Accessed 12/4/2018. http://www.archive.org/stream/algebraandtrigon033520mbp#page/n70/mode/1up/search/range. Buy the book
  3. Goldrei, D.C.. Classic Set Theory: For Guided Independent Study. pg 5. Chapman & Hall Mathematics. July 1, 1996. Last Accessed 12/4/2018. Buy the book
  4. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pp 13-14. Thomson, Brooks/Cole. 2005. Buy the book

Cite this article as:

McAdams, David E. Range. 4/30/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/r/range.html.

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Revision History

4/30/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
12/4/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (McAdams, David E.)
12/31/2008: Changed equations from HTML to images. Corrected example range from y>0 to y>=0 (McAdams, David E.)
12/23/2008: Added figure 1. (McAdams, David E.)
9/4/2008: Added 'More Information'. (McAdams, David E.)
4/22/2008: Added reference to range of a function. (McAdams, David E.)
2/27/2008: Converted javascript vocabulary hot links to html. (McAdams, David E.)
7/12/2007: Initial version. (McAdams, David E.)

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