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Definition: The absolute value of a number is the distance between that number and 0.  

Rule: To show that we want the absolute value of a number, we put straight lines around it.

Interactivity: Absolute Value    Directions for Interactivity

  Click and drag the big blue point.

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Examples                         

  • The distance between two points is always a positive value.
  • This means, the absolute value of a number is always positive.

In the above image, there is a number line and 4 points Ѕ W Y Z and in the image below is shown the way to calculate the absolute value

  • The point Z represents the number 26.  The distance between Z and 0 is 26 (see below)  

So the absolute value of 26 is 26. We write this sentence: |26| =26 .

  • Look at the point Y. Do you see that |19| =19 ?  

Now, let's look at the points to the left of 0.  

  • The point W represents the number -7, but the distance between W and 0 is 7.

So the absolute value of –7 is 7 or |-7| =7 .

  • Look at the point Ѕ. Do you see that |-25| =25 ?

The graph of y=|x|

x y=|x|
0 |0|=0
1 |1|=1
-2 |-2|=2

The graph of y=2|x|+1

x y=2|x|+1
0 2|0|+1=0+1=1
1 2|1|+1=2+1=3
-2 2|-2|+1=4+1=5

The graph of y=-|x|+2

x y=-|x|+2
0 -|0|+2=0+2=2
1 -|1|+2=-1+2=1
-3 -|-3|+2=-3+2=-1

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Page last modified on March 17, 2008, at 02:21 PM