MS Algebra A-F-IF-1 Ch. 5.1 Functions as Ordered Pairs. Mr. Deyo Represent Functions as Ordered Pairs with a Domain and a Range

Transcription

1 MS Algebra A-F-IF-1 Ch. 5.1 Functions as Ordered Pairs Mr. Deyo Represent Functions as Ordered Pairs with a Domain and a Range

2 Title: 5.1 Functions as Ordered Pairs Date: Learning Target By the end of the period, I will represent a function as a set of ordered pairs with a domain { x } and a range { f(x) }. I will demonstrate this by completing Four- Square Notes and by solving problems in a pair/group activity.

3 Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder? 2) Section 5.1 Pg ) Section TxtBk. Prob. #5-15 Odd,26-30 Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder? Table of Contents Date Description Date Due

4 Storm Check (Think, Write, Discuss, Report) Questions on which to ponder and answer: 1. How are the two images similar? 2. How are they different? 3. How can these two images be related to math?

5 Daily Warm-Up Exercises For use with pages xxx xxx Write an expression: 7 more than a number x. Gabe spent $4 more than twice as much as Casey at a store. If Casey spent $6, how much did Gabe spend?

6 Daily Warm-Up Exercises For use with pages xxx xxx Write an expression: 7 more than a number x. ANSWER x + 7 Gabe spent $4 more than twice as much as Casey at a store. If Casey spent $6, how much did Gabe spend? ANSWER G = 4 + 2C G = 4 + 2(6) G = or 7 + x G = $16

7 1) Relation Vocabulary 2) Domain 3) Range 4) Function 5) Independent Variable (x) 6) Dependent Variable f(x) or y

8 Sketch DAY 2 1. Review word Friendly Definition Physical Representation 2. Draw a sketch Wordwork DAY 3 and/or DAY 4 1. Review the word Friendly Definition Physical Representation 2. Show how the word works Synonyms/antonym Word Problems Related words/phrases Example/non-example Word List Friendly Definition DAY 1 1. Use Visuals 2. Introduce the word Friendly Definition Physical Representation 3. Use Cognates 4. Write friendly definition 5. Physical Representation DAY 5 1. Review the word Friendly definition Physical Representation Sentence 3. Write a sentence at least 2 rich words (1 action) correct spelling correct punctuation correct subject/predicate agreement clear and clean writing

9 Notes: x Rule f(x) Function Machine

10 Problem A Identify the domain and range of a relation Amount (gallons) Cost (dollars) The table shows the cost of various amounts of regular unleaded gas from the same pump. a. Write the table as a set of ordered pairs. b. Identify the domain and range of the relation.

11 Problem A Identify the domain and range of a relation Amount (gallons) Cost (dollars) The table shows the cost of various amounts of regular unleaded gas from the same pump. a. Write the table as a set of ordered pairs. SOLUTION b. Identify the domain and range of the relation. The table can be written as {(10, 29.99), (12, 35.99), (13, 38.99), (17, 50.98)}. The domain is 10, 12, 13, 17. The range is 29.99, 35.99, 38.99,

12 Problem B Identify the domain and range of the relation: {(-1, 9), (0, 4), (3, 1), (8, -2)} Domain: Range:

13 Problem B Identify the domain and range of the relation: {(-1, 9), (0, 4), (3, 1), (8, -2)} ANSWER Domain: -1, 0, 3, 8 Range: -2, 1, 4, 9

14 ALL CLASS Multiple Choice Practice Which relation is a function? { (0, -2), (0, 3), (5, -4), (10, 5) } { (0, -1), (1, 2), (4, 8), (6, 12) } { (0, 7), (-1, 7), (-2, 7), (-2, 8) } { (-2, 9), (4, 7), (4, 5), (6, -3) }

15 ALL CLASS Multiple Choice Practice SOLUTION Choices A, C, and D are not functions because each relation contains a domain element that is paired with two different range elements. For instance, 0 is paired with both -2 and 3 in choice A. The relation { (0, -1), (1, 2), (4, 8), (6, 12) } in choice B is a function because each domain element is paired with exactly one range element. ANSWER The correct answer is B.

16 Storm Check (Think, Write, Discuss, Report) How does a relation qualify as a function? A relation qualifies as a function when.

17 Title: 5.1 Functions as Ordered Pairs Date: Learning Target By the end of the period, I will represent a function as a set of ordered pairs with a domain { x } and a range { f(x) }. I will demonstrate this by completing Four- Square Notes and by solving problems in a pair/group activity.

18 Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder? 2) Section 5.1 Pg ) Section TxtBk. Prob. #5-15 Odd,26-30 Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder? Table of Contents Date Description Date Due

19 Problem A Write a function rule Write a rule for the function. x y Rule Function Machine

20 Problem A Write a function rule SOLUTION Write a rule for the function. x y Notice that each output y is 2 more than the corresponding input x. So, a rule for the function is y = x + 2.

21 Problem B Write a function rule SOLUTION Write a rule for the function. x y Rule Function Machine

22 Problem B Write a function rule SOLUTION Write a rule for the function. x y Rule y = 2x Function Machine

23 Problem A Write a function rule for a real-world situation CONCERT TICKETS You are buying concert tickets for that cost $15 each. 1) Write the total cost (in dollars) of the tickets as a function of the number of tickets you buy. 2) Identify the independent and dependent variables. 3) How much would 6 tickets cost?

24 Problem A Write a function rule for a real-world situation CONCERT TICKETS SOLUTION You are buying concert tickets for that cost $15 each. 1) Write the total cost (in dollars) of the tickets as a function of the number of tickets you buy. 2) Identify the independent and dependent variables. 3) How much would 6 tickets cost? Write a verbal model. Then write a function rule. Let T represent the number of tickets bought and C represent the total cost (in dollars). 1) The function rule is C = 15T. 2) The total cost depends on the tickets bought, so T is the independent variable and C is the dependent variable. 3) Six tickets would cost 15(6) or $90.

25 Problem B Time (hours) Pay (dollars) ) Write a rule for the function. 2) Identify the Independent Variable 3) Identify the Dependent Variable 4) ** Identify the domain and the range.

26 Problem B ANSWER Time (hours) Pay (dollars) ) Write a rule for the function. P = 8T 2) Identify the Independent Variable T: Time 3) Identify the Dependent Variable P: Pay 4) ** Identify the domain and the range. 1, 2, 3, 4 8, 16, 24, 32

27 1) Relation Vocabulary 2) Domain 3) Range 4) Function 5) Independent Variable (x) 6) Dependent Variable f(x) or y

28 Title: 5.1 Functions as Ordered Pairs Date: Learning Target By the end of the period, I will represent a function as a set of ordered pairs with a domain { x } and a range { f(x) }. I will demonstrate this by completing Four- Square Notes and by solving problems in a pair/group activity.

29 Home Work 1-2-3: 1) Class 4-Square Notes Put In Binder? 2) Section 5.1 Pg ) Section TxtBk. Prob. #5-15 Odd,26-30 Notes Copied on blank sheet Solved and Put in Binder? of paper in Binder? Table of Contents Date Description Date Due

30 Ticket OUT. Identify the domain and range of the relation { (3, -2), (6, 4), (7, -1), (10, 1) } Determine whether the relation is a function. { (-1, 4), (2, 5), (2, 9), (4, -4) }

31 Ticket OUT. Identify the domain and range of the relation { (3, -2), (6, 4), (7, -1), (10, 1) } ANSWER domain: 3, 6, 7, 10 range: -2, -1, 1, 4 Determine whether the relation is a function. { (-1, 4), (2, 5), (2, 9), (4, -4) } ANSWER NOT a function each domain element is NOT paired with exactly one range element