Absolute Value

1
Chapter 4

• Section 2
• Absolute Value

2
Line Formulas
3
Absolute Value

• Absolute value is a measure of magnitude or
  distance. It is therefore always a positive
  value.

4
The Piecewise Definition

• Please sketch a graph of it.

5
More Compact Version

• Graph using calculator

6
Determine the Piecewise Definition

• First, set the expression inside the absolute
  value bars equal to 0 and solve.
• Next, determine the sign of the expression (x
  2) on each side of 2. Use a number line to
  assist.
• Now we remove the absolute value bars.

7
Your Turn

• Determine a piecewise definition of the following
  absolute value function.

8
Examples

• Convert the following into a piecewise defined
  function.

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Use Your Calculator

• Graph the following on the same coordinate grid

10
Chapter 4

• Section 3
• Absolute Value Equations

11
Types of Solutions

• Given the equation there are 3 possibilities
  for solutions depending on the sign of a
• Case 1 a lt 0
• Case 1 a 0
• Case 1 a gt 0

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13
Solve the following both graphically and
algebraically
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Use the Graphical TechniquethenUse the
Algebraic Technique

• Solve