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Domain and Range

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Date: 08/25/97 at 12:50:17
From: Jenni
Subject: Pre-Cal

Hi. I'm a junior in high school and I need help with my pre-cal.

I don't understand what we are doing  in class. Can you explain about
Domain and Range? I don't get it. I also have problems with Piecewise
Function, Notation, Boolean Test, Transformation on Fraction,
Operation on Function, Compositions of functions, and domain of
composite.

Thanks.
```

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

Hi Jenni -

The basic concept of domain and range is pretty simple.  Here are the
facts:

- The domain of a function is the set of all the stuff you can
plug into the function.

- The range of a function is the set of all the stuff you can
get out of the function.

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.

Let's try another example: f(x) = 1/(x-5).

What numbers can we plug into this function?  Well, it looks like any
number will do. But wait! What happens if we plug in 5?  We divide by
zero, and the world blows up. So let's not plug in 5. Since any other
number is fine, the domain of this function is: all real numbers
except 5.

What's the range?  I'll leave that one to you.

Here's an anonymous tip. In general, when you're trying to find the
domain of a function, there are two things you should look out for.
They are:

(1) Look for potential division by zero.
(2) Look for places where you might take the square root
of a negative number.

Since these are the two easiest ways to make the world blow up, these
are the things you really have to watch out for.

For your other questions, you can look around in the calculus and
pre-calculus pages in our archives. Two good pages to start looking
at are

High School Calculus
http://mathforum.org/library/drmath/sets/high_calculus.html

High School Functions
http://mathforum.org/library/drmath/sets/high_functions.html

There's lots of good stuff there.  Good luck with it!

-Doctor Ken,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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Associated Topics:
High School Functions

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