Associated Topics || Dr. Math Home || Search Dr. Math

### Domain and Range of Functions

Date: 03/20/2003 at 20:35:32
From: Jimmy Neutron
Subject: Domain and range

I am learning in school about the domain and range of functions. Why
are they called domain and range? And where did they come from?

Date: 03/20/2003 at 23:37:05
From: Doctor Peterson
Subject: Re: Domain and range

Hi, Jimmy.

"Domain" and "range" are just two different words for "how far
something extends"; specifically, a king's domain is the territory he
controls, and an animal's range is the region it wanders through. So
it makes some sense that the set of numbers a function "controls"
would be called its domain, and the set through which its value can
wander is called its range.

To be more precise, Merriam-Webster, at m-w.com, defines the words
(in the most relevant usage) this way:

Domain 2 : a territory over which dominion is exercised
5 : the set of elements to which a mathematical or logical
variable is limited; specifically : the set on which a
function is defined

(The word comes from the Latin word for "lordship".)

Range  3 a : a place that may be ranged over b : an open region
over which animals (as livestock) may roam and feed c : the
region throughout which a kind of organism or ecological
community naturally lives or occurs
8 a : the set of values a function may take on b : the
class of admissible values of a variable

(Several other uses are similar, such as the range of a weapon or a
voice; the original meaning comes from the idea of animals ranging

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
Associated Topics:
High School Definitions
High School Functions
Middle School Definitions

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search