December 05, Ch4.notebook. Objective: To learn how to analyze and write function rules. Warm Up 11/30. Nov 30 7:36 AM

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1 Objective: To learn how to analyze and write function rules. Warm Up 11/30 Nov 30 7:36 AM 1

2 Objective: To learn how to analyze and write function rules. Warm Up 12/1 Dec 1 7:37 AM 2

3 Objective: To learn how to analyze and write function rules. To learn and solve equations using function notation. Warm Up: Pop Quiz On the given note card, write your name and then answer each of the following questions to the word problem! Your total cost C for hiring a garden designer is $200 for an initial consolation plus $45 for each hour h the designer spends drawing plans. 1) What is a function rule that represents this situation? 2) What is the INDEPENDENT VARIABLE for this situation? 3) What is the DEPENDENT VARIABLE for this situation? Dec 2 9:37 AM 3

4 HW WS Answers (Page 6) 1) Function all inputs go to exactly 1 output 2) Function all inputs go to exactly 1 output 3) Function all inputs go to exactly 1 output 4) Not a Function the input value of 2 goes to 5 and 1 5) Function all inputs go to exactly 1 output 6) Function the graph passes the V.L.T. 7) Not a Function the graph fails the V.L.T. 8) Not a Function the input value of 2 goes to 0 and 3 Nov 30 7:37 AM 4

5 HW Answers (page 7 & 8) Dec 2 2:31 PM 5

6 Dec 5 11:49 AM 6

7 Dec 5 2:31 PM 7

8 Classwork: Nov 30 7:48 AM 8

9 Chapter 4: An Introduction to Functions (4.1, 4.2, 4.5, 4.6) A is a pairing of numbers from the domain and the range o The variable for the domain is called the since it can be any number o The variable for the range is called the since it depends on the domain A is a relation in which each member of the is paired with exactly one member of the Four ways to represent a function Ordered Pairs (2,4), (3, 5), ( 5, 6) (5, 8) Charts x y Domain: Range: Domain: Range: Mapping Graphing Domain: Domain: Range: Range: Nov 2 8:00 AM 9

10 To Be or Not to Be a Function A function may not have two y values assigned to the same x value o (2,4), (2,6) BAD A function can have two x values assigned to the same y value o (2,4), (3,4) GOOD Use vertical line test to tell on a graph!! Nov 2 9:05 AM 10

11 Function each x has only one y Function each x has only one y (0,2), (1,4), (3,5), (1,8) Not a function 1 has two y outputs Function each x has only one y Not a function x has more than one y (FAILS vertical line test!) Function each x has only one y (passes vertical line test) Not a function x has more than one y (FAILS vertical line test!) Not a function 2 has two y values Nov 2 11:17 AM 11

12 Analyzing a Function Rule Function rule express the dependent variable in terms of the independent variable Is the following a function. If not, explain or show with a counterexample. Example 1: Domain: {letters}, Range: {boy names} Rule: For each letter inputted, the output is a boy s name Example 2: Domain: {girl names}, Range: {letters} Rule: For each girls name inputted, the output is the first letter of the name Example 3: Domain: {months}, Range: {numbers} Rule: For each month inputted, the output is the number of days in the month. Example 4: Domain: {Holidays}, Range: {Months} Rule: For each holiday inputted, the output is the month Nov 2 9:05 AM 12

13 Writing a Function Rule Example 1: Write a function rule to represent: y is 5 less than the product of 4 and x Example 2: You can estimate the temperature by counting the number of chirps of the snowy tree cricket. The outdoor temperature is about 40ºF more than one fourth the numbers of chirps the cricket makes in one minute. What is a function rule that represents this situation? Example 3: a) A kennel charges $15 per day to board dogs. Upon arrival, each dog must have a flea bath that costs $12. Write a function rule for the total cost for n days of boarding plus a bath. b) How much does a 10 day stay cost? Nov 2 9:06 AM 13

14 ADDITIONAL NOTES PAGE Nov 30 2:05 PM 14

15 Dec 2 9:36 AM 15

16 Function Notation f(x) = o Examples: Nov 2 12:14 PM 16

17 Dec 2 2:26 PM 17