Domain and Range

"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.1

1.http://mathforum.org/library/drmath/view/62497.htm

Domain represents all the x values, and Range represents all the y values. List the x and y values without duplication.

Ex: State the Domain and Range of the following relation.

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

Domain: {2, 3, 4, 6}
Range: {–3, –1, 3, 6}

http://www.purplemath.com/modules/fcns2.htm

What is a function?
If you can solve for “y”, then it is a function or if you can enter it into your graphing calculator. You can also tell if it’s a function by using the vertical line test. If it crosses through the graph twice, it is not a function.

1. This one is a function because there is no vertical line that will cross this graph twice.

2. This one is not a function because any number of vertical lines will intersect this oval twice. For instance, the y-axis intersects twice.
http://www.purplemath.com/modules/fcns.htm

Finding the Domain

The domain of a function is the set of numbers that you can put into the function and get out something that makes sense.

Ex: f(x) = (4+x)/(x^2-9)

(1) If we put in 4, we get f(4) = (4+4)/(4^2 - 9) = 8/7.

(2) If we put in 0, we get f(0) = (4+0)/(0^2 - 9) = 4/-9 = -(4/9)

(3) If we put in 3, we get f(3) = (4+3)/(9-9) = 7/0

You can't divide by 0, so 7/0 is an answer that doesn't make sense, and that f(x) is not defined at x = 3 and the same for x = -3. You will always get a fraction out of this function. (If you get a whole number n, you can think of it as the fraction n/1.) The only fractions that are undefined are those with 0 in their denominators.

This means that the function is undefined only at these two numbers, so its domain is all real numbers but 3 and -3.

http://mathforum.org/library/drmath/view/54554.html