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8.1 Relations And Functions
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8.1 Relations And Functions

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Chapter 8, Section 1: Relations and Functions.

Chapter 8, Section 1: Relations and Functions.

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