Introduction to Absolute Value
Expressions and Graphs
Absolute Value
An Official Definition: x 
x
2
Absolute value makes
things positive.
Practical Definition:
The absolute value of x, denoted x , is regarded as
the distance of x from zero. This is why absolute
Read “The absolute
value
is
never
neg
ati
v
e
.
value of -7.”
Example: Evaluate 7  7
Notice :
7 7
7
-10
-5
0
5
10
Arithmetic with Absolute Value
In order to evaluate an expression containing an absolute
value, the absolute value part needs to be simplified
first. Treat the absolute value like parentheses.
Example: Evaluate
4 2  3  15  7
4 6  15  7
Absolute value makes
things positive.
4 9  7
Evaluate the expression
inside the absolute value
first. Do NOT use the
Distributive Property.
4  9   7
36  7
29
IF you use the awful acronym PEMDAS to evaluate expressions. It can be
extended to APEMDAS (evaluate the absolute value expression before
parentheses).
Absolute Value in the Calculator
The calculator will calculate Absolute Value.
Instead of the absolute value bars the
calculator uses the abbreviation abs( ).
•
•
•
Hit MATH
Hit the right arrow button for the NUM
category
Press enter on 1:abs(
Absolute Value Graph
Always make a table.
Connect the points.
x
y
-4
4
-3
3
-2
2
-1
1
0
0
1
1
2
2
3
3
4
4
All “linear” absolute value
graphs will have a “V” shape.
Graphing a 2 Variable Inequality
Graphically represent the solutions to the following inequality:
Solid or Dashed?
y  2x 1
Find the Boundary
Plot points for the equality
y  2x 1
Test Every Region
(0,0)
0  2  0 1
0<1
True
Pick a point
in each
region
Substitute
into
Original
Shade True
Region(s)
(0,2)
2  2  0 1
2<1
False