properties of real numbers objective: review properties of real numbers

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Properties of Real Numbers Objective: Review Properties of Real Numbers.

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Unbounded Intervals on the Real Number Line Notation Interval Type Inequality Graph x > a Open x > a x < b Open x < b Entire real line

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Page 1: Properties of Real Numbers Objective: Review Properties of Real Numbers

Properties of Real Numbers

Objective: Review Properties of Real Numbers.

Page 2: Properties of Real Numbers Objective: Review Properties of Real Numbers

Bounded Intervals on the Real Number Line

• Notation Interval Type Inequality Graph• [a, b] Closed a < x < b

• (a, b) Open a < x < b

• [a, b) a < x < b

• (a, b] a < x < b

Page 3: Properties of Real Numbers Objective: Review Properties of Real Numbers

Unbounded Intervals on the Real Number Line

• Notation Interval Type Inequality Graph• x > a

• Open x > a

• x < b

• Open x < b

• Entire real line

),( a

),[ a

),( b

],( b

),( x

Page 4: Properties of Real Numbers Objective: Review Properties of Real Numbers

Definition of Absolute Value• The absolute value of a number is its magnitude, or

its distance from zero. Distance is always positive, so absolute value is always positive.

Page 5: Properties of Real Numbers Objective: Review Properties of Real Numbers

Definition of Absolute Value• The absolute value of a number is its magnitude, or

its distance from zero. Distance is always positive, so absolute value is always positive.

• If a is a real number, then the absolute value of a is

if a > 0 if a < 0

,,||aaa

Page 6: Properties of Real Numbers Objective: Review Properties of Real Numbers

Properties of Absolute Value

1) |a| > 0

2) |-a| = |a|

3) |ab| = |a||b|

4) =||||ba

ba

Page 7: Properties of Real Numbers Objective: Review Properties of Real Numbers

Distance Between Two Points on the Real Number Line

• Let a and b be real numbers. The distance between a and b is:

d(a, b) = |b – a| = |a – b|

Page 8: Properties of Real Numbers Objective: Review Properties of Real Numbers

Read• Review all of the rules of algebra on Pages 6-8. You

are responsible for knowing all of these.

Page 9: Properties of Real Numbers Objective: Review Properties of Real Numbers

Homework

• Pages 9-10• 11-59 odd• 79, 81, 83