Graphs of Absolute Value Equations
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Key Questions

Let's start with a simple one
#y=x+2# If
#x> 2# ,#x+2# is positive, so#y=x+2=x+2#
If#x<2# ,#x+2# is negative, but will be 'turned around' by the abslote signs, so in this domain#y=x+2=x2# These two semigraphs meet at
#(2,0)#
graph{x+2 [10.5, 9.5, 1.08, 8.915]} 
The shape of a graph with an absolute value would look something similar to a "V".
graph{abs(x) [10, 10, 5, 5]}
This graph has a slope of
#1# on the right of the#y# =axis and#1# on the left of the#y# axis 
#y = a abs(xh)+k# has vertex#(h, k)# #y = 3 abs(x1)+5# has vertex#(1, 5)# 
A table of values is simply a pairing between an input and an output. Absolute value equations can range from very complex to relatively simple  there are also many theorems and postulates that dictate the behavior of absolute value equations in various circumstances.
In its purest form, absolute value makes all numbers positive. For instance,
# y = x # would result in the positive form of#x# being the output, whether#x# is positive or negative. For instance, if#x# is#5# , it would be#5# when it comes out of that equation. Create a table of values like you normally would, but compute values enclosed in absolute value markers as positive.Another common form of absolute value equations can be found in a form similar to
#a3 = 5# Thus:
#a3 = 5# would have#a# values# 2 < x < 8 # From there, you can create a table from the values of
#a# .If you can update your question with more detail, I may be able to answer it better.
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Linear Inequalities and Absolute Value

1Inequality Expressions

2Inequalities with Addition and Subtraction

3Inequalities with Multiplication and Division

4MultiStep Inequalities

5Compound Inequalities

6Applications with Inequalities

7Absolute Value

8Absolute Value Equations

9Graphs of Absolute Value Equations

10Absolute Value Inequalities

11Linear Inequalities in Two Variables

12Theoretical and Experimental Probability