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Algebra II

Algebra II. Intervals and Interval Notation. Intervals. The set of all numbers between two endpoints is called an interval. An interval may be described either by an inequality , by interval notation , or by a straight line graph . An interval may be: Bounded :

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Algebra II

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  1. Algebra II Intervals and Interval Notation

  2. Intervals • The set of all numbers between two endpoints is called an interval. • An interval may be described either by an inequality, by interval notation, or by a straight line graph. • An interval may be: • Bounded: • Open - does not include the endpoints • Closed - does include the endpoints • Half-Open - includes one endpoint • Unbounded: one or both endpoints are infinity

  3. Graphing Intervals • Set A with endpoints 1 and 3, neither endpoint included 1------3 • Set B with endpoints 6 and 10, not including 10 6 -----10 • Set C with endpoints 20 and 25, including both endpoints 20------25 • Set D with endpoints 28 and infinity, not including 28 28------ • Set E with endpoints 28 and infinity, including 28 28 ------

  4. Inequality Examples: • Set A with endpoints 1 and 3, neither endpoint included 1 < x < 3 • Set B with endpoints 6 and 10, not including 10 6 x < 10 • Set C with endpoints 20 and 25, including both endpoints 20 x 25 • Set D with endpoints 28 and infinity, not including 28 28 < x < • Set E with endpoints 28 and infinity, including 28 28 x <

  5. Interval Notation • A parenthesis ( ) shows an open (not included) endpoint • A bracket [ ] shows a closed [included] endpoint Examples: • Set A with endpoints 1 and 3, neither endpoint included (1,3) • Set B with endpoints 6 and 10, not including 10 [6,10) • Set C with endpoints 20 and 25, including both endpoints [20,25] • Set D with endpoints 28 and infinity, not including 28 (28, )

  6. Interval Notation A union U combines sets Example: Sets A + B + C + D is written as (1,3) U [6,10) U [20,25] U (28, )

  7. Inequality, Interval Notation, and Corresponding Graph An interval may include: • Neither endpoint – Open Interval Example: all numbers between six and ten, but not 6 nor 10 6 < x< 10 or (6,10) or 6------10 • One endpoint – Half-open Interval Example:all numbers between six and ten, but not 6 6 < x 10 or (6,10] or 6-----10 • Both endpoints – Closed Interval Example: all numbers between six and ten, including 6 and 10 6 x 10 or [6,10] or 6------10

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