1. Name:________________________________________________________________________________Date:_____/_____/__________ Fill-in-the-Blanks: 1)A relation is a _______________ of ordered pairs. 2)A ________________________ is a special type of relation, where every x value has one and only one y value (the relationship between x and y remains consistent). 3)In a function, the x value can never ___________________. 4)Fill-in-the-table: 5)What is the domain of the following relation? { (-2, 4); (0, 8); (2, 12); (4, 16) } D = ____________________________________________ Are the following relations functions? Answer “yes” or “no” : 6) _____ 7)_____ 8)_____ 9) _____ {(-1, 5); (0, 5); (1, 5); (2, 5)} 10)_____ {(3, 7); (5, 11); (7, 15); (3, 10)} xy Input Domain Dependent xy -84 -44 04 44 xy -22 00 22 44 xy -42 00 4-2 0-4

2. Plot each point in order, connecting the points with a line. Tip: Make the line as you plot the points– don’t wait until the end. 11) 12) What are the four ways to represent a function? 1. Equation (y = 2x + 5) 2._________3._________4.________

3. Today’s Lesson: What: Function tables Why: Given a function table, to represent said table as an equation and as a graph. What: Function tables Why: Given a function table, to represent said table as an equation and as a graph. Input Output

4. 4) Let’s write this “rule” as an equation:_____________ 1 2 3 Consider the following pattern: 1)The above represents a toothpick pattern. How many toothpicks would be in Figure #4? ________ 2) Fill-in-the-table: Figure # (x) # of Toothpicks (y) 13 2 3 4 5 6 3)Is there an easy way to see how many toothpicks we would need for Figure #100? 12 9 6 15 12 18 Yes ! There is a “times 3” rule going from x to y, so we would need 300 toothpicks! y = 3x We can say that the # of Toothpicks is a function of the Figure #. “y” depends on “x.”

5. Sometimes it is helpful to think of a Function table as an input/output “Machine”... 5) As the inputs (x values) and outputs (y values) are revealed, can you figure out the “machine rule”? Input (x) Output (y) Rule: Equation: 0 3 14 25 3 6 47 “plus 3” y = x + 3 50 53

6. 6) Input (x) Output (y) 14 27 310 4 5 Rule: Equation: 13 16 “times 3, plus 1” y = 3x +1 100 301

7. 7) Input (x) Output (y) 11 23 35 4 5 Rule: Equation: Every input/output is an ordered pair, so it is easy to graph... 7 9 “times 2, minus 1” y = 2x - 1 Notice the straight line. We will be studying linear functions during this unit. They will ALL graph as a straight line! 40 79

8. “Toothpick Patterns Lab” Wait for directions from teacher...

9. We will now continue our regular lesson, so get your notes back out...

10. (x)(y) 14 26 38 4 5 Is there a shortcut? Yes... I call it The “magic number” shortcut... Step One: Find the pattern going down the “y” column. This is the magic number ! Step Two: The magic number tells you what to multiply x by! Our magic # is __________. Step Three: See if you need a second step... Final Equation: y = 2x + 2 There is a +2 pattern going down the y column... 10 12 2 So, the first part of the equation is 2x... When we multiply our “x” numbers by 2, we see that we still need to add 2 in order to equal “y.” Catch– the “magic” only works if your inputs are in a row!!

11. 8) Let’s tie it all together (use the shortcut to help You)... Table:Equation: Graph: (x)(y) 0-2 11 24 3 4 7 10 + 3 pattern... y = 3x - 2

12. 9) Table:Equation: Graph: (x)(y) 00 1-2 2-4 3 4 -6 -8 - 2 pattern... y = -2x This is a subtraction pattern going down “y.” This means the magic # is negative!

13. (x)(y) 2-4 3 42 5 6 10) Table:Equation: Graph: 5 8 +3 pattern... y = 3x - 10 Your turn...

14. 11) Table:Equation: Graph: - 4 pattern... y = -4x - 2 (x)(y) -310 -26 2 0 1 -2 -6 This is a subtraction pattern going down “y.” This means the magic # is negative! Your turn...

15. (x)(y) 36 47 58 6 7 Table:Equation: Graph: 12) 9 10 +1 pattern... y = x + 3 When the pattern going down “y” is “plus 1,” it means that the equation does not need a multiplication step. Your turn...

16. IXL: 7 th Grade V.6 & V.10 homework

17. END OF LESSON The next slides are student copies of the notes and/or handouts for this lesson. These were handed out in class and filled-in as the lesson progressed.

18. Math-7 NOTES DATE: ______/_______/_______NAME: What: Function tables Why: Given a function table, to represent said table as an equation and as a graph. What: Function tables Why: Given a function table, to represent said table as an equation and as a graph. 1 2 3 Consider the following pattern: 1)The above represents a toothpick pattern. How many toothpicks would be in Figure #4??_________ 2) Fill-in-the-table: Figure # (x) # of Toothpicks (y) 13 2 3 4 5 6 3)Is there an easy way to see how many toothpicks we would need for Figure #100? 4) Let’s write this “rule” as an equation: _______________ Sometimes it is helpful to think of a Function table as an put/output “Machine”... 5) As the inputs (x values) and outputs (y values) are revealed, can you figure out the “machine rule” (fill in numbers as they are revealed)? Input (x) Output (y) Rule: Equation:______________

19. 6) Input (x) Output (y) 14 27 310 4 5 Rule: Equation:______________ 7) Every input/output is an ordered pair, so it is easy to graph... Input (x) Output (y) 11 23 35 4 5 Rule: Equation:______________ Graph for #7... Time for “toothpick patterns” lab (wait for directions)...

20. (x)(y) 14 26 38 4 5 Is there a shortcut? Yes... I call it The “magic number” shortcut... Step One: Find the pattern going down the “y”column. This is the magic number ! Step Two: The magic # tells you what to multiply x by! Our magic # is __________. Step Three: See if you need a second step in order to equal y... ________________ Final Equation: __________________________ There is a +2 pattern going down the y column... 8) Let’s tie it all together (use the shortcut to help You)... Table: Equation:___________________________ Graph: (x)(y) 0-2 11 24 3 4 Table: Equation:___________________________ Graph: (x)(y) 00 1-2 2-4 3 4 9) When there is a subtraction pattern, the “magic number” is negative!!

21. Table: Equation:___________________________ Graph: (x)(y) 2-4 3 42 5 6 Your turn... 10) Table: Equation:___________________________ Graph: (x)(y) -310 -26 2 0 1 11) IXL: 7 TH Grade, V.6 & V.10 Find the pattern going down the “y” column. This is the magic #! Multiply this # to x!! Table: Equation:___________________________ Graph: (x)(y) 36 47 58 6 7 12) This is a subtraction pattern going down “y.” This means the magic # is negative! When the pattern going down “y” is “plus 1,” it means that the equation does not need a multiplication step.

22. 1)Extend the Toothpick pattern below. How many toothpicks are in Figure # 4 ? _____ 1 2 3 4 (draw below) 2)Use the pattern in #1 to complete the below table. List the # of toothpicks in each figure. 3)Is it possible to have a figure with 40 toothpicks? Explain. 4)How many toothpicks would be in Figure # 20? 5)The # of toothpicks increases by 4 each time. This is a “+4” pattern for the (y) column in the above table. What is the pattern (or rule) for going from (x) to (y)? 6)Use your answer to #5 in order to write the equation for finding the number of toothpicks (y) given the figure number (x): y = Figure # (x) # of Toothpicks (y) 12 2 3 4 5 6 “Toothpick Patterns Lab” Name:__________________________________________________________________ Date:_____/_____/__________

23. EXIT TICKET “Toothpick Patterns Lab” NAME:_________________________________________________________________________________DATE: ______/_______/_______ 1) In the function table featured in the lab, the “x” column stood for the Figure #. What did the “y” column stand for? 2) This is the same table from the lab: Write the equation here: __________________________________________________ 3. How many toothpicks would be required to build Figure # 100? Figure # (x) # of Toothpicks (y) 12 26 310 414 518 622

24. 1)2)3) Directions: Fill in the missing spaces in the below function tables. Then, write the equation: (x)(y) -2-10 -5 00 1 2 xy =_______ (equation) Name: _______________________________________________ Date:_____/_____/__________ (x)(y) 03 15 27 4 5 xy= _______ (equation) (x)(y) -310 -27 4 0 1 xy =_______ (equation) 4)5)6) (x)(y) 630 734 838 9 10 xy =_______ (equation) (x)(y) 04 10 2-4 4 5 xy= _______ (equation) (x)(y) -60 -51 -32 -2 xy =_______ (equation) “Equations from Tables” Math-7 PRACTICE Find the pattern going down the “y” column. This is the magic #! Multiply this # to x!! If it is a subtraction pattern, the magic # is negative!!

25. 7) Fill-in-table AND graph: (x)(y) 02 15 28 3 4 Xy =_______ (equation)