1	Algebra Review - Intervals
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: Finite: Open - does not include the endpoints Closed - does include the endpoints Semi-Infinite - includes one endpoint Infinite: one or both endpoints are infinity
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, ) A union U combines sets Example: Sets A + B + C + D is written as (1,3) U [6,10) U [20,25] U(28, )
5	Graphing Intervals Set A with endpoints 1 and 3, neither endpoint included ₁m------m₃ Set B with endpoints 6 and 10, not including 10 ₆l-----m₁₀ Set C with endpoints 20 and 25, including both endpoints ₂₀l------l₂₅ Set D with endpoints 28 and infinity, not including 28 ₂₈ m------ Set E with endpoints 28 and infinity, including 28 ₂₈l------
6	Inequality, Interval Notation, and Corresponding Graph An interval may include: Neither endpoint - open set Example: all numbers between six and ten, but not 6 nor 10 6 < x < 10 or (6,10) or ₆m------m₁₀ One endpoint Example: all numbers between six and ten, but not 6 6 < x 10 or (6,10] or ₆m-----l₁₀ Both endpoints - closed set Example: all numbers between six and ten, including 6 and 10 6 x 10 or [6,10] or ₆l------l₁₀