Functions - Teacher Copy - Absolute

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Absolute Value Functions

September 16th, 2011

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The Concept

The absolute value of a real number is its value with itssign removed.

The number is placed between vertical lines to signify thatwe are to ignore its sign.

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Properties

The absolute value

can never equal anegative

The absolute of a positiveequals the absolute of thenegative

The absolute of a productof two values equals the

product of their absolutes

The absolute of quotientMiss Connell


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An Absolute Situation

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The Basic AbsoluteValue

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For the Visual Learner

Interactive Graph

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http://www.shodor.org/interactivate/activities/GraphSketcher/http://www.shodor.org/interactivate/activities/GraphSketcher/


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The loss of Parameter b

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The Transformed A.V.F.

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Parameters -PropertiesMiss Connell


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Remember

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Drawing the Graph

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Practice

Reflections Textbook:

Page 73 # 1-10

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September 21, 2011

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Absolute Value

Functions


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Drawing the Graph

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Sketching the Graph

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Zeros and Equations

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Zeros Example

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Zeros Example

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Zeros Example

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Zeros Example

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Zeros and Equations

Steps:

1. Isolate the absolute value2. Check if the equation has solutions (does the R.S. equal a

positive or negative?)

3. Split the absolute into two cases: The positive and The

Negative

4. Solve the resulting two equations with respect to thecritical value

5. Deduce the solution set from the equation or the zeros ofthe function.

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Finding the Rule

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Example

Find the Rule of the Function:

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Point (2, 3)Vertex (0,2)


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Example

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Sign

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Inequalities

The solution set of an inequality with an absolute value

1. May be an interval or the union of intervals

2. May be a single value (one solution)

3. May be empty (no solution)

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Inequalities

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Inequalities

Steps:

1. Isolate the absolute2. Determine the region (interior or exterior)

3. The value opposite the absolute (on the other sign of the

inequality symbol) is considered the critical value

4. Split into 2 cases: The Positive and the Negative (same asan equality)

5. Draw your number line

6. Apply the values found7. Represent the solutions on a number line

a) Use open points if the equation is NOT part of the inequality

b) Use closed points if it IS a part of the inequality (or equal tos)

8. Write our solution setMiss Connell


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Example

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Critical Value = 0


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Example

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Critical Value = 7


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September 21, 2011

Practice Reflections Text

Page 80 #2, 5, 7, 8

Page 88 # 6, 7, 9

Page 93 # 1 - 6

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Functions - Teacher Copy - Absolute

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