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/
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