2.2 Absolute Value

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2.2 Absolute Value

• Goal Find the opposite and the absolute value of
  a number

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Absolute value- A numbers distance from zero on
the number line.
-5 -4 -3 -2 -1 0 1 2 3 4
5
0
3
12
5
5.4
-7
10
-16
-23
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Opposites vs. Absolute Value
Given Number
Opposite
Absolute Value
8
- 8
-24
24
-3.5
3.5
4
Solve each equation below.
1)
4)
no solution
x 10 or -10
2)
5)
x 14 or - 14
x 4 or - 4
3)
6)
x 0
3
3
t or -
4
4
5
Determine whether each statement is true always,
sometimes, or never for all real numbers.
1)
4)
sometimes
never
2)
5)
always
sometimes
3)
6)
sometimes
always
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Velocity vs. Speed
Velocity - Indicates speed and direction.
Speed - The absolute value of velocity.
Example
A helicopter descends at 50 feet/second.
A) What is its velocity?
-50 ft./sec.
B) What is its speed?
50 ft./sec.
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Counterexamples
To prove a statement true, it must be proven
true for all examples - difficult!
An example that proves a statement false.
Counterexample -
Statement All pets are furry.
Counterexample Goldfish.
Statement
Counterexample
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Determine whether each statement is true or false
for all real numbers. If it is false, find a
counter-example that proves it is false.
1)
4)
False, x 0
True
2)
5)
False, x -7
True
3)
6)
False, x -5
True