Intervals and Interval Notation 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
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 ------
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 <
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, )
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, )
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