Absolute Value Function

What is the area of the region bounded by the graph of |x+y|+|x-y|=4?
Source: NCTM Mathematics Teacher, October 2006

Solution
If x+y>0 and x-y>0
|x+y|+|x-y|=4
(x+y)+(x-y)=4
2x=4
x=2
image
If |x+y|<0 and |x-y|<0
|x+y|+|x-y|=4
-(x+y)-(x-y)=4
-x-y-x+y=4
-2x=4
x=-2
image
If |x+y|>0 and |x-y|<0
|x+y|+|x-y|=4
(x+y)-(x-y)=4
x+y-x+y=4
2y=4
y=2
image
If |x+y|<0 and |x-y|>0
|x+y|+|x-y|=4
-(x+y)+(x-y)=4
-x-y+x-y=4
-2y=4
y=-2
image
The four graphs intersect and form a square of side length 4.
image
The are of the square equals 16.

Solution: 16 square units

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About mvtrinh

Retired high school math teacher.
This entry was posted in Problem solving and tagged , , , , , , , . Bookmark the permalink.

One Response to Absolute Value Function

  1. Deepak Suwalka says:

    It’s a nice post about absolute value function. I really like it. It’s really helpful. Thanks for sharing it.

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