Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

8.1 Relations And Functions

Chapter 8, Section 1: Relations and Functions.

Related Books

Free with a 30 day trial from Scribd

See all
  • Be the first to comment

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>

×