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Interval Notation

Interval Notation. Today you will be introduced to interval notation. Warm-Up. Solve each of the inequalities. Write your answer as an inequality and graph the solution on a number line. 1. 4x + 5 > 25 2. 5 – 5x > 4(3 – x) 3. –16 < 3x – 4 < 2 4. –2 < -2n + 1 < 7

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Interval Notation

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  1. Interval Notation Today you will be introduced to interval notation.

  2. Warm-Up Solve each of the inequalities. Write your answer as an inequality and graph the solution on a number line. 1. 4x + 5 > 25 2. 5 – 5x > 4(3 – x) 3. –16 < 3x – 4 < 2 4. –2 < -2n + 1 < 7 5. 3x + 2 < -10 or 2x – 4 > -4

  3. Types of Sets • Set: a collection of elements and its symbol is { } • Subset: a part of a set. • Disjoint Sets: two sets are disjoint if they have no elements in common. • Empty Set: If a set contains no items it is called the empty set or the null set. Symbol: 

  4. Interval Notation Subsets of real numbers are placed in interval notation. • Open Intervals: (a,b) = {x: a < x < b} • Closed Intervals: [a,b] = {x: a < x < b} *a and b are referred to as endpoints. In open intervals, endpoints are NOT included whereas in closed intervals, the endpoints are included.  refers to infinity - refers to negative infinity

  5. Bounded & Unbounded Intervals Bounded Intervals: have two specific endpoints. Example: [-2, 10] or (-2, 10) or (-2,10] Unbounded Intervals: one or no specific endpoint. Example: (-, 10] or (-2, ) or (-, )

  6. Unions & Intersections • Union: the union of two sets A and B is the set of elements that are members of A or B or both. Symbol: AB “or” • We use the term UNION, , to unite multiple intervals.

  7. Intersections • Intersection: the intersection of two sets A and B is the set of elements that are members of BOTH A and B. Symbol: AB “and” • We use the term INTERSECTION, , to discuss the overlap of multiple intervals.

  8. Types of Notation We use three different types of notation to represent intervals in mathematics: • interval notation • algebraic (or inequality) notation • a number line graph *You should be able to easily go from one notation to another.

  9. Try These: I. Represent each of the following in interval notation and on a number line. 1. –6 < x < 1 2. x < 4 3. 0 < x < 5 4. x > 2 5. –5 < x < 3

  10. Try These: II. Represent each of the following in inequality notation and on a number line. 6. [-3,2] 7. (4,7) 8. [-3,6) 9. (-, -1] 10. (7, )

  11. Try These: III. Represent each of the following in inequality notation and in interval notation.

  12. Try These: III. Represent each of the following in inequality notation and in interval notation.

  13. Try These: III. Represent each of the following in inequality notation and in interval notation.

  14. Practice with Unions IV. Find each union or intersection and then represent the result in interval notation. 16. (-2,1] [4,6] • [3,4)[6, ) • (-, -3] (-2, )

  15. Back to the Warm-Up We can also represent the answers to the inequalities that we completed in the warm-up in interval notation. 1. 4x + 5 > 25 2. 5 – 5x > 4(3 – x) 3. –16 < 3x – 4 < 2 4. –2 < -2n + 1 < 7 5. 3x + 2 < -10 or 2x – 4 > -4

  16. Assignment • Complete supplemental worksheet • Cover book

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