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# Pre Cal Notes 1 1

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### Pre Cal Notes 1 1

1. 1. CHAPTER 1 FUNDAMENTALS
2. 2. Notes 1-1: Real Numbers CA State Standards: Alg 1 1.0, Alg 2 25.0
3. 3. Sets and Intervals <ul><li>A set is a collection of objects. </li></ul><ul><li>The objects are called the elements of the set. </li></ul><ul><li>a є S means a is an element of set S. </li></ul><ul><li>b є S means b is not an element of set S. </li></ul><ul><li>You can describe a set by listing its elements in braces. A = {1,2,3,4,5} </li></ul><ul><li>You could also describe it in set-builder notation </li></ul><ul><li>A = {x | x is an integer and 1 ≤ x ≤ 5} </li></ul>
4. 4. <ul><li>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. </li></ul><ul><li>The intersection of S and T, S ∩ T, is the set containing all the elements that are in both S and T. </li></ul><ul><li>The empty set , Ø , is the set that contains no elements. </li></ul>
5. 5. Ex 1: Given S = {1,2,3,4,5} , T= {4,5,6,7}, and V = {6,7,8} <ul><li>Find S υ T </li></ul><ul><li>Find S ∩ T </li></ul><ul><li>Find S ∩ V </li></ul>S υ T = {1,2,3,4,5,6,7} S ∩ T = {4,5} Ø
6. 6. <ul><li>An interval is a set that corresponds to line segments. </li></ul><ul><li>The open interval from a to b is denoted (a,b) and contains all of the integers between a and b. </li></ul><ul><li>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. </li></ul><ul><li>Let’s look at the chart on page 7 for more examples… </li></ul>
7. 7. Ex 2. Write each interval in set-builder notation, then graph. <ul><li>[-1,2) </li></ul><ul><li>[1.5, 4] </li></ul><ul><li>(-3, ∞) </li></ul>= { x| -1 ≤ x < 2} = { x| 1.5 ≤ x ≤ 4} = { x| -3 < x }
8. 8. Ex 3. Find and graph S∩T if S=(2,5) and T = [4,7] <ul><li>S∩T = </li></ul>
9. 9. Ex 4. Evaluating Absolute Value <ul><li>|3|= </li></ul><ul><li>|-3| = </li></ul><ul><li>|0| = </li></ul><ul><li>|3 -  | = </li></ul>3 3 0 -(3 -  ) = -3 +  =  - 3
10. 10. Ex 5. Distance between points on the number line. <ul><li>Find the distance between -8 and 5. </li></ul>
11. 11. today’s assignments… <ul><li>Notes 1-1 Q & S </li></ul><ul><li>CW 1-1 Page 11 # 36 – 72 even </li></ul>