Algebra II Intervals and Interval Notation Intervals The

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: • Open - does not include the endpoints • Closed - does include the endpoints • Half-Open - includes one endpoint – Unbounded: one or both endpoints are infinity 2

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 -----3

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< 4

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, ) 5

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, ) 6

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 7