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### Graphing f(2x) and f(|x|)

```Date: 09/03/2003 at 00:25:28
From: Tim
Subject: Graphing f(2x) and f(|x|)

I cannot comprehend how to graph f(2x) and f(|x|).

In the first, do you multiply the values by two? That doesn't seem to
make sense when it is graphed.

In the second, making all the x values positve causes some points to
overlap each other.

Can you help?
```

```
Date: 09/04/2003 at 10:07:05
From: Doctor Marshall
Subject: Re: graphing f(2x) and f(|x|) functions

Dear Tim,

If we know the value of f(x) for some domain of x, then the
function f(2x) is simply the value x=2k _at_ the point x=k for all k
in x.

This may sound confusing! If so a picture is a great way to see
what happens here:

________   |
f(x)   /        \  |
___*/          \_|__
/                 |  \
____/____|______|______|___\_________
/    2k      k      |    \
/                    |     \
|
* denotes (2k,f(2k))

f(2x)
___  |
/   \ |
__*/   \_|_
/         | \
_____________/__|______|_\____________
/   k      |  \
/          |  \
|

* denotes (k,f(2k))

As for f(|x|), for any value x greater than or equal to 0, f(|x|)
is just f(x). For negative values of x, the value of f(|x|) is just
the corresponding f(-x) (-x being a positive number now). If you draw
a picture of this you will see that this absolute value operator
effectively takes a function, truncates (i.e., removes) the x<0
portion and replaces it with a reflection of f through the y axis

I hope this helps, feel free to write back to Dr. Math with more
questions!

- Doctor Marshall, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Equations, Graphs, Translations
High School Functions

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