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### 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

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/
```
Associated Topics:
High School Functions

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