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 
about.)

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

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/