1. Function Function Notation: f(x) = 3x + 5 Rule for Function

2. Function Set up a table using the rule: f(x)= 3x+5 x(Input)12345 y(Output)8

3. Function Evaluate this rule for these x values: f(x)= 3x+5 So 3(2) + 5 = 11… x(Input)12345 y(Output)811141720

4. Patterns Patterns are functions. They’re predictable.

5. Patterns with Triangles Jian made some designs using equilateral triangles, as shown below. He noticed that as he added new triangles, there was a relationship between n, the number of triangles, and p, the outer perimeter of the design. Jian made some designs using equilateral triangles, as shown below. He noticed that as he added new triangles, there was a relationship between n, the number of triangles, and p, the outer perimeter of the design. from the MCAS P=3 P= 4 P=5 P=6

6. Number of Triangles Outer Perimeter (in units) 1 3 2 4 3 5 4 6... … N p (in units) 1 3 2 4 3 5 4 6... … N p from the MCAS P = 3 P = 4 P = 5 P = 6

7. Triangles * Write a rule for finding p, the outer perimeter for a design that uses n triangles. from the MCAS P= 3 P= 4 P= 5 P= 6 P = 3P = 5

8. How to Write a Rule: 1) Make a table. 2) Find the constant difference. 3) Multiply the constant difference by the term number (x). 4) Add or subtract some number in order to get y. 5) Check your rule for at least 3 values of x. *Does it work?

9. # of Triangles Outer Perimeter # of Triangles Outer Perimeter (in units) 1 3 (in units) 1 3 2 4 2 4 3 5 3 5 ** The constant difference is +1. So multiply x by 1 So multiply x by 1 then add 2 then add 2 to get the output number. to get the output number. from the MCAS P=3 P=4 P=5 P= 6

10. f(x)= X + 2 So evaluate and you get: 2+1= 3; 2+2 = 4; and 3+2 = 5. It works! P = 3 P= 4 P = 5 P = 6

11. Brick Walls Brick Walls What’s my rule? from the MCAS Now you try one:

12. How to Write a Rule: 1) Make a table. 2) Find the constant difference. 3) Multiply the constant difference by the term number (x). 4) Add or subtract some number in order to get y. 5) Check your rule for at least 3 values of x. *Does it work?

13. Steps x f(x) or y 17 213 319 The constant difference is +6, so the rule is 6x + 1.

14. Steps You can see the You can see the constant difference. You’re adding 6 blocks each time. 6 blocks

15. Patterns in Tables A city planner created a table to show the total number of seats for different numbers of subway cars. Copy the table. What is the rule? What is the rule? from the MCAS

16. Subway Cars Subway Cars Number of Subway Cars Total Number of Seats 6180 8240 10 10300 …… ns from the MCAS First, make a table…

17. Subway Cars f(x) = 30x

18. Try it! Write a rule that describes the relationship between the input (x) and the output (y) in the table below. Write a rule that describes the relationship between the input (x) and the output (y) in the table below. Input (x) 251011 Output (y) 5112123 from the MCAS

19. Input / Output Table f(x)=2x + 1 f(x)=2x + 1

20. Patterns in Real-life Situations Lucinda earns $20 each week. She spends $5 each week and saves the rest. The table below shows the total amount that she saved at the end of each week for 4 weeks. Lucinda earns $20 each week. She spends $5 each week and saves the rest. The table below shows the total amount that she saved at the end of each week for 4 weeks. What’s the rule? What’s the rule? from the MCAS

21. Lucinda’s Savings f(x) = $15x from the MCAS

22. Write a rule for the cost of n rides: from the MCAS

23. Fall Carnival f(x) = $10 + $2x

24. Patterns in Real-Life Situations: Patterns in Real-Life Situations: The local library charges the same fine per day for each day a library book is overdue. The table below shows the amount of the fine for a book that is overdue for different numbers of days. Fines for Overdue Library Books 246… Amount of Fine $0.30$0.60$0.90… from the MCAS What’s the rule? What do they charge for 1 day?

25. Library Fines f(x) = $0.15x f(x) = $0.15x from the MCAS

26. Patterns in Sequences of Numbers: 12, 16, 20, 24… What’s my rule?

27. Patterns in Sequences of Numbers f(x) = 4x + 8 f(x) = 4x + 8