Range and Domain of a Graph

Date: 02/12/99 at 12:27:31
From: Eric Nava
Subject: The Range and Domain of a Graph

If the graph of a function "f" is shown, determine the domain and range 
of "f". The text has a line starting at (-2,3) and going down to (0,0). 
Could you help me?

Date: 03/05/99 at 12:09:46
From: Doctor Teeple
Subject: Re: The Range and Domain of a Graph

To help your understanding, here is a graph of what I think your 
function looks like:

   

When you think of a function, you should think of the two parts. One 
part of the function is the input and the other part is the output. In 
other words, the role of a function is to take a number, do some sort 
of transformation, and give back another number. This is easier to see 
when we write the function as something like:

   f(x) = 3x + 6

For example, we could input a 2 to get:

   f(2) = 3*2 + 6 = 12

There are plenty of other numbers that we could input. All of these 
numbers make up the domain. All of the output numbers are called the 
range.

In some cases, we may want to define the domain to be only certain 
numbers. For example, we could say that the domain for f(x) above is 
just the set {2, 3, 4}. Then we are allowed to evaluate the function at 
these three points only. At any other number, we do not know what the 
output would be. So if we ask, what is f(3), we know it is f(3) = 
3*3 + 6 = 15. But if we ask, what is f(5), we do not know. The function 
f is not defined at that point. 

What is the range of the function f(x) with domain {2, 3, 4}? It is 
all of the possible output values. We know that we can get 12 and 15 as 
output values. Evaluate the function at 4, and you will see that 18 is 
also a possible output value. So the range is {12, 15, 18}.

Now, your function is presented in a different way. It is presented as 
a graph, but the definitions of domain and range are still the same. 
Ask, what are the values where I know that f(x) is defined? In this 
case, it is all of the x values, which go from -2 to 3. I just got 
these values by looking at the graph. Then ask, given this domain, what 
are the possible output values? I will leave this for you to do. Please 
write back if you need more help with this. 

I looked in the archives for some other resources to help you with the 
domain and range concepts. Try:

   Function Machine
   http://mathforum.org/library/drmath/view/54541.html    

   Domain and Range
   http://mathforum.org/library/drmath/view/54551.html   

   Functions: Domain, Range, and Piecewise
   http://mathforum.org/library/drmath/view/54570.html   

Please write back if you need help on this or anything else.

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