Unit 4 Chapter 5: Relations and Functions

Transcription

1 Unit 4 Chapter 5: Relations and Functions 1

2 What you should already know... Grade 8 > You represented Linear Relations using ordered pairs, table of values and graphs Grade 9 > You wrote an expression or equation given pictorial, oral or written form of the relation. > You graphed linear relations > You used interpolation and extrapolation to solve problems > Discrete and Continuous Data > Independent and Dependent Variables 2

3 Section 5.1: Representing Relations 6 Ways to Describe a Relation: Words Ordered Pairs Table of Values Graphs Equations Arrow Diagrams Review Ex.) A photography studio charges a booking fee of $15 and $8 for each sheet of pictures ordered. Use C as the total cost and p for sheets of pictures ordered. Use the Frayer Model below to represent the relation. 3

4 Do we connect points on a graph? Discrete Data: Data values on a graph that are. This is because the values in between them have no meaning. (A finite number of points exists between any two other values.) Continuous Data: Data values on a graph that are. The values between points have meaning. (An infinite number of points exists between any two other values.) 4

5 IN GRADE 9 Relation > A rule that relates two quantities, the independent and dependent variables. The independent variable was the x value, the first coordinate in an ordered pair. The dependent variable was the y value, the second coordinate in an ordered pair. Independent (x, y) Dependent 5

6 In Math 1201 we need to extend the definition of relation (p.257) to state: a rule that associates the elements of one set with elements in another set. It associates the independent variable with a dependent variable. A set is a collection of distinct objects. An element of a set, is one object in the set You can write a set in a list using brackets. For example {banana, apple, pear, strawberry} is a set. What is the relation in this set? 6

7 A relation can also be represented using an arrow diagram. Steps: 1. Take two sets and arrange them separately(in alphabetical or numerical order) in ovals. 2. An arrow is drawn to associate the element in the first set with an element in the second set. 3. State the association or relation on top of the arrow. Element of first set association Element of second set 7

8 Kobe Bryant is a well known basketball player. Each year he is given a base salary of $ and is paid $ each game he plays. Use an arrow diagram to describe this relationship. Games Salary This would read 0 games played he will get paid. 2 games played he will get paid. It does not make sense to go backwards: $ he will get paid 3 games A relation has the direction from one set to the other set only! 8

9 Representing Relations 1. Animals can be associated with the classes they are in. Animal Ant Eagle Snake Turtle Whale Class Insect Aves Reptilia Reptilia Mammalia Pull A) Describe this relation in words. The relation shows the association belongs to the class between a set of animals and a set of classes. Pull B) Represent this relation as i) a set of ordered pairs {(ant, Insecta), (eagle,aves), (snake, Reptilia) (turtle,reptilia), (whale,mammalia)} ii) as an arrow diagram 9

10 2. A) Describe the relation represented by the bar graph. Pull The relation shows the association "average travel time, in hours" from different cities in BC to Vancouver. B) Represent this relation: i) as a table Do questions 3 5, 7, 9, 10, pages

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12 Attachments notebook 8122.galleryitem