Pre Cal Notes 1 1
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This document provides an introduction to fundamental concepts in algebra including sets, intervals, unions, intersections, and absolute value. It defines what sets, elements, unions, and intersections are. It explains the differences between open, closed, and empty intervals. Examples are provided to demonstrate finding unions and intersections of sets, writing intervals in set-builder notation, finding intersections of intervals, evaluating absolute values, and calculating distances on the number line. Students are assigned related questions and a worksheet to practice these concepts.
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![An interval is a set that corresponds to line segments. The open interval from a to b is denoted (a,b) and contains all of the integers between a and b. The closed interval from a to b is denoted [a,b] and contains all of the integers between a and b including a and b themselves. Let’s look at the chart on page 7 for more examples…](https://image.slidesharecdn.com/precalnotes1-1-100225110139-phpapp01/85/Pre-Cal-Notes-1-1-6-320.jpg)
![Ex 2. Write each interval in set-builder notation, then graph. [-1,2) [1.5, 4] (-3, ∞) = { x| -1 ≤ x < 2} = { x| 1.5 ≤ x ≤ 4} = { x| -3 < x }](https://image.slidesharecdn.com/precalnotes1-1-100225110139-phpapp01/85/Pre-Cal-Notes-1-1-7-320.jpg)
![Ex 3. Find and graph S∩T if S=(2,5) and T = [4,7] S∩T =](https://image.slidesharecdn.com/precalnotes1-1-100225110139-phpapp01/85/Pre-Cal-Notes-1-1-8-320.jpg)
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Pre Cal Notes 1 1
- 2. Notes 1-1: Real Numbers CA State Standards: Alg 1 1.0, Alg 2 25.0
- 3. Sets and Intervals A set is a collection of objects. The objects are called the elements of the set. a є S means a is an element of set S. b є S means b is not an element of set S. You can describe a set by listing its elements in braces. A = {1,2,3,4,5} You could also describe it in set-builder notation A = {x | x is an integer and 1 ≤ x ≤ 5}
- 4. If S and T are sets, then their union S υ T is the set of all elements in either S or T or both. The intersection of S and T, S ∩ T, is the set containing all the elements that are in both S and T. The empty set , Ø , is the set that contains no elements.
- 5. Ex 1: Given S = {1,2,3,4,5} , T= {4,5,6,7}, and V = {6,7,8} Find S υ T Find S ∩ T Find S ∩ V S υ T = {1,2,3,4,5,6,7} S ∩ T = {4,5} Ø
- 6. An interval is a set that corresponds to line segments. The open interval from a to b is denoted (a,b) and contains all of the integers between a and b. The closed interval from a to b is denoted [a,b] and contains all of the integers between a and b including a and b themselves. Let’s look at the chart on page 7 for more examples…
- 7. Ex 2. Write each interval in set-builder notation, then graph. [-1,2) [1.5, 4] (-3, ∞) = { x| -1 ≤ x < 2} = { x| 1.5 ≤ x ≤ 4} = { x| -3 < x }
- 8. Ex 3. Find and graph S∩T if S=(2,5) and T = [4,7] S∩T =
- 9. Ex 4. Evaluating Absolute Value |3|= |-3| = |0| = |3 - | = 3 3 0 -(3 - ) = -3 + = - 3
- 10. Ex 5. Distance between points on the number line. Find the distance between -8 and 5.
- 11. today’s assignments… Notes 1-1 Q & S CW 1-1 Page 11 # 36 – 72 even