1 / 19

Pre Calculus Sec 1.1 Real Numbers

Pre Calculus Sec 1.1 Real Numbers. Objectives: To review the set of Real Numbers To review the properties of Algebra To understand interval and set notation. Real Numbers. Natural Numbers: 1,2,3,4,…  Integers: -,…-3,-2,-1,0,1,2,3,…

ruby
Download Presentation

Pre Calculus Sec 1.1 Real Numbers

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Pre CalculusSec 1.1 Real Numbers Objectives: To review the set of Real Numbers To review the properties of Algebra To understand interval and set notation.

  2. Real Numbers • Natural Numbers: 1,2,3,4,… • Integers: -,…-3,-2,-1,0,1,2,3,… • Rational Numbers: any # that can be written as a ratio of integers (as a fraction). • Irrational Numbers: any # that cannot be written as a fraction.

  3. CLASS WORK • Given the set, list the elements of the set that are: • Natural numbers • Integers • Rational numbers • Irrational numbers

  4. Properties of Real Numbers Commutative Property: a + b = b + a ab = ba order doesn’t matter Associative Property: (a+b)+c = a+(b+c) (ab)c = a(bc) order doesn’t change

  5. Distributive Property: a(b+c) = ab + ac you can add then multiply or multiply then add.

  6. CLASS WORK State the property of real numbers being used. 2. 3. 4.

  7. Sets & Elements • A set is a collection of objects. - the objects are called the elements of the set. If S is a set, the notation of means that a is an element of S.

  8. Sets & Elements means that b is not an element of S. Ex1. If Z represents the set of integers, then but

  9. Notation of Sets • Braces { } - The set A that consists of positive integers less than 7 is • Set-builder notation – • Interval notation – These are sets of real numbers and correspond geometrically to line segments.

  10. Union of Sets • If S and T are sets, then , represents their union. The union of sets consists of all elements in both sets. Ex 2. Find if

  11. Intersection of Sets • The intersection of S and T is the set consisting of all elements that are in both sets. It is only what they have in common. Ex 3. Find if

  12. Ex 4. Find, , ,

  13. CLASS WORK If find: 5. 6. 7.

  14. CLASS WORK If find 8. 9. 10.

  15. Intervals b b

  16. Ex. 5 Express each interval in terms of inequalities then graph the interval. • [-1, 2) • [1.5, 4] • (-3, )

  17. CLASS WORK Express each interval in terms of inequalities then graph the interval. 11. [2, 8) • (-, -5)

  18. CLASS WORK Express the inequality in interval notation, then graph the interval. 13. 14.

  19. HW p. 10 1-9 odd, 33,34,35-59 odd

More Related