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. The absolute value of the number is the length of the purple line segment.

This browser does not have a Java Plug-in.
Get the latest Java Plug-in here.


  • 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 ?

Attach:ab_val6.jpg Δ

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

Related Topics


ACT GR 20-23




 Up one level

Page last modified on December 13, 2008, at 01:59 AM