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/