properties of real numbers objective: review properties of real numbers
DESCRIPTION
Unbounded Intervals on the Real Number Line Notation Interval Type Inequality Graph x > a Open x > a x < b Open x < b Entire real lineTRANSCRIPT
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
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
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.
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
Properties of Absolute Value
1) |a| > 0
2) |-a| = |a|
3) |ab| = |a||b|
4) =||||ba
ba
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|
Read• Review all of the rules of algebra on Pages 6-8. You
are responsible for knowing all of these.
Homework
• Pages 9-10• 11-59 odd• 79, 81, 83