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# 8.1 Relations And Functions

Chapter 8, Section 1: Relations and Functions.

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### 8.1 Relations And Functions

1. 1. Chapter 8 Section 1: Relations and Functions February 4 th , 2009
2. 2. What two forms of information is being illustrated? Write in your Notes!
3. 3. Graph 1: The Population of New York City, 1790-1840
4. 5. Food for Life Canned Food Drive The information in this chart can be written as an ordered pair , also known as a RELATION. 150 21 106 74 20 105 195 22 104 148 24 103 216 22 102 133 25 101 Number of Cans Number of Students Home-room
5. 6. Relation  Ordered Pair <ul><li>In the case of the Food Drive, the number of Students is the X coordinate and the Number of Cans is the Y coordinate. </li></ul><ul><li>Room 101: (25, 133) </li></ul><ul><li>Room 102: (22, 216) </li></ul><ul><li>Room 103: (24, 148) </li></ul>Y X 150 21 106 74 20 105 195 22 104 148 24 103 216 22 102 133 25 101 Number of Cans Number of Students Home-room
6. 7. They’re All Related <ul><li>If all you have is a bunch of ordered pairs , you know they belong to the same RELATION if they’re in braces, or these things { }. </li></ul><ul><li>*Back to the Relation* </li></ul><ul><li>(Domain, Range) </li></ul><ul><li>The first number is called the DOMAIN. </li></ul><ul><li>The second number is called the RANGE. </li></ul>
7. 8. Some Relations are Functions <ul><li>If the DOMAIIN is PAIRED with EXACTLY ONE member of the RANGE , then the Relation is a FUNCTION. </li></ul><ul><li>A Mapping Diagram can be used to determine if your Relation is really a Function . </li></ul>
8. 9. Mapping Diagram <ul><li>{(0,1), (1,2), (1,3), (2,4)} </li></ul><ul><li>List the domain values and the range values in order. </li></ul><ul><li>Draw arrows from the domain values to their range values. </li></ul><ul><li>There are two range values for the domain value of 1. Therefore, this relation is NOT a function. </li></ul>
9. 10. So, If You Missed It The First Time. <ul><li>One range value for each domain value, then the relation is a function. </li></ul><ul><li>More than one range value for each domain, then the relation is NOT a function. </li></ul>
10. 11. Make a Map, Is it a Function? <ul><li>{(0,1), (1,2), (2,2), (3,4)} </li></ul><ul><li>{(0,1), (1,3), (2,2), (3,4)} </li></ul><ul><li>{(-2, 3), (2,2), (2, -2)} </li></ul><ul><li>{(-5, -4), (0, -4), (5, -4)} </li></ul>Is a Function Is a Function Is NOT a Function Is a Function
11. 12. Real Life: Thinking, Instead of Math <ul><li>Is the time needed to cook a turkey a function of the weight of the turkey? </li></ul><ul><li>The time the turkey cooks (RANGE VALUE) is determined by the weight of the turkey (DOMAIN VALUE). This relation is a function. </li></ul>
12. 13. Try These <ul><li>For the United States Postal Service, is package weight a function of the postage paid to mail the package? </li></ul><ul><li>NO; a specific postage cost (Domain) can mail packages of different weights (Range). </li></ul><ul><li>When building a wooden structure, is the amount of wood needed a function of the height of the building? </li></ul><ul><li>YES; the higher the building, the more wood you need. </li></ul>
13. 14. Graphing Relations and Functions <ul><li>By graphing a RELATION on a Coordinate Plane, you can SEE whether a Relation is really a FUNCTION. </li></ul><ul><li>Once you’ve graphed the Relations, IF the graph PASSES the Vertical Line test , then it’s a FUNCTION . </li></ul><ul><li>If the graph does NOT pass the Vertical Line test, then the Relation is NOT a Function . </li></ul>
14. 15. This is the Vertical-Line Test… <ul><li>Graph each coordinate in the Relation. </li></ul><ul><li>Pass a pencil across the graph. Keep the pencil vertical (parallel to the Y-axis) to represent the vertical line. </li></ul><ul><li>If the pencil covers up more than one point (one ordered pair) at once, then the RELATION is NOT a FUNCTION. </li></ul>Pencil passes (2,0) and (2,3), so this relation is NOT a function. -4 5 3 4 3 2 0 2 -3 -4 Range Domain
15. 16. Come to the Board <ul><li>Graph these Relations, is it a function or not, according to the Vertical-Line Test. </li></ul>3 4 7 5 0 1 -2 0 -2 -3 -5 -6 Range Domain 5 0 5 1 3 -1 -1 -1 6 -2 4 -7 Range Domain 4 1 4 2 0 0 4 -3 4 -4 4 -5 Range Domain
16. 17. Assignment #1 <ul><li>Assignment #1: </li></ul><ul><li>Pages 389-390: 1-23 all, 28, 29. </li></ul><ul><li>If it asks for an example or explanation, you MUST give one! </li></ul><ul><li>A good way to explain is to give the two ordered pairs that make the relation NOT a function. </li></ul>