Connecting Table, Graph, & Function Notation Common Core #4, #13, #22, #25-26, & #29

Connecting Table, Graph, & Function Notation Lakeshia is a science team member and a computer whiz. Ms. Alvarez, the language teacher, is going to pay Lakeshia $10 upfront and $6 an hour to keep her computer records current. Ms. Alvarez will only pay Lakeshia for whole hours only. (1) In this situation, what variables might affect what Lakeshia earns? Answers will vary but will surely include the number of hours worked.

Connecting Table, Graph, & Function Notation (2) Complete the following table. Number of Hours Process Column Money Earner 1 2 3 4 5 10 15 20

Connecting Table, Graph, & Function Notation (2) Complete the following table. Number of Hours Process Column Money Earned 1 10 + 1(6) 16 2 10 + 2(6) 22 3 10 + 3(6) 28 4 10 + 4(6) 34 5 10 + 5(6) 40 10 10 + 10(6) 70 15 10 + 15(6) 100 20 10 + 20(6) 130

Connecting Table, Graph, & Function Notation (3) Describe in words a pattern you see in the money earned column. Number of Hours Process Column Money Earned 1 10 + 1(6) 16 2 10 + 2(6) 22 3 10 + 3(6) 28 4 10 + 4(6) 34 5 10 + 5(6) 40 10 10 + 10(6) 70 15 10 + 15(6) 100 20 10 + 20(6) 130

Connecting Table, Graph, & Function Notation (3) Describe in words a pattern you see in the money earned column. Lakeshia earns $10 plus $6 times n where n is the number of hours worked. Number of Hours Process Column Money Earned 1 10 + 1(6) 16 2 10 + 2(6) 22 3 10 + 3(6) 28 4 10 + 4(6) 34 5 10 + 5(6) 40 10 10 + 10(6) 70 15 10 + 15(6) 100 20 10 + 20(6) 130

Connecting Table, Graph, & Function Notation (4) In this scenario, what is the independent variable? What is the dependent variable? Answers are independent variable is the number of hours she works and the dependent variable is the amount of money she earns.

Connecting Table, Graph, & Function Notation (5) Lakeshia is naturally concerned with how many hours she will work and how much money she will make. Write a sentence with these variables using “depends on” or “is a function of”. Possible Answer: The amount of money earned is a function of how many hours are worked.

Connecting Table, Graph, & Function Notation (6) Choose meaningful letters for your variables and write a function rule for the how much Lakeshia will earn. Possible Answer: m = 10 + 6h or e = 10 + 6n (7) How much will Lakeshia earn for working 14 hours? Answer is $94. (8) How long would Lakeshia have to work to earn $130? Answer is 20 hours.

Connecting Table, Graph, & Function Notation (9) The algebraic equation m = 10 + 6h can also be written in function notation. The expression M(h) is read the function M of h. Rewrite your expression using function notation. You may need to Google it. Possible Answer: M(h) = 10 + 6h or E(n) = 10 + 6n (10) We often use substitution in algebra. Find M(7) & M(11). Answers are M(7) = 52 and M(11) = 76

Connecting Table, Graph, & Function Notation (11) Which of the following values for h are meaningful for this situation. Explain your reasoning. h = 6 h = 11 h = 3.7 h = 0 h = 2⅙ Answers could vary some but since Ms. Alvarez is only willing to pay Lakeshia for whole hours worked, 3.7 and 2⅙ are not meaningful here. Some may argue that 0 is not meaningful as well.

Connecting Table, Graph, & Function Notation (12) The set of numbers you chose that are meaningful for h is also know as the DOMAIN. h = 6 h = 11 h = 3.7 h = 0 h = 2⅙ See if you can write the domain for this function and explain your reasoning. M(h) = 10 + 6h You may gave to use Google again Answers should be all whole numbers which could also be written {0, 1, 2, 3, 4, …….}