Domain and range

What is domain and range?
- The domain of a function is the set of all the stuff you can
plug into the function. The domain of a function is the set of all real numbers for which the function is defined.To find the domain, ask yourself the following questions: What can x not be? or Where does this function have an illegal operation?

- The range of a function is the set of all the stuff you can
get out of the function.The range of the function is the set of all values assumed by the dependent variable(y).To find the range, ask yourself the following question: What are all possible values of y?

http://www.math.ksu.edu/~mxw0000/final/domran.html

Let's do an example: f(x) = x^2 (that's x squared)

What's the domain? Well, you can plug any old real number you want
into this function: I can square 4, or -7, 1.01738, or whatever, and
the world doesn't blow up.

What's the range? Well, let's think about it. If I plug any number
into this function, am I ever going to be able to get a negative
number out of it? Nope! (Unless you're dealing with imaginary numbers,
and I bet you're not!) So it looks like the range of this function is
the set of all non-negative numbers (the positive numbers plus zero).
And in fact, that's the right answer.

Date: 08/25/97 at 13:36:18From: Doctor KenSubject: Re: Pre-Cal


The Domain of a Functions is: The set of possible x-values (independent variable)
The Range of a Functions is: The set of possible y-values (dependent variable)
e.g. F = { (1, 3), (2, 5), (3, 10), (4, 17)}
The Domain of the function F is {1,2,3,4}
The Range of the function F is {3,5,10,17}

http://math.clackamas.cc.or.us/kyser/math111/ch2/22stuff/sol2.htm

Definition of the Domain of a Function
For a function f defined by an expression with variable x, the implied domain of f is the set of all real numbers variable x can take such that the expression defining the function is real. The domain can also be given explicitly.
Definition of the Range of a Function
The range of f is the set of all values that the function takes when x takes values in the domain.

Domain: The domain of a function is the set of all possible input values (usually x), which allows the function formula to work.

Most often a function's domain is all real numbers. Consider a simple linear equation like the graph shown below. What values are valid inputs? Every number! It's range is all real numbers because there is nothing that won't work. The graph extends forever in the x directions.
What kind of functions don't have a domain of all real numbers? The kinds of functions that aren't valid for particular input values.

Range: The range is the set of all possible output values (usually y), which result from using the function formula.

The range of a simple linear function is almost always going to be all real numbers. A graph of a line, such as the one shown below on the left, will extend forever in either y direction. There's one notable exception: y=constant. When you have a function where y equals a constant (like y=3), your graph is a horizontal line. In that case, the range is just that one value. Otherwise, the range is all real numbers.
Many other functions have limited ranges. While only a few types have limited domains, you will frequenty see functions with unusual ranges.