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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

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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.________

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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

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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.”

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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 1 13 25 3 7 49 “times 2, plus 1” y = 2x + 1 50 101

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6) Input (x) Output (y) 13 27 311 4 5 Rule: Equation: 15 19 “times 4, minus 1” y = 4x - 1 100 399

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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!

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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:_____/_____/__________

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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

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(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!!

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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

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9) Table:Equation: Graph: (x)(y) 12 24 36 4 5 8 10 + 2 pattern... y = 2x

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END OF LESSON The next slides are student copies of the notes for this lesson. These notes were handed out in class and filled-in as the lesson progressed. NOTE: The last slide(s) in any lesson slideshow represent the homework assigned for that day.

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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:______________

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6) Input (x) Output (y) 13 27 311 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...

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(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) 12 24 36 4 5 9)

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“Equations from Patterns” Math-7 PRACTICE/ Homework NAME:__________________________________________________________________________________________________________DATE:_____/_____/__________ 1. Using the pattern in the chart, how many toothpicks would be needed for a figure with 5 hexagons? __________ 2.Consider the second column of numbers written as a sequence: 6, 11, 16, 21... Is there a common difference? __________ So, this is an example of which type of sequence?______________________________________ 3.How many toothpicks would be needed for a figure with 10 hexagons?_____ 4. If the Number of Hexagons column represents “x” and the Number of Toothpicks column represents “y,” write an equation that describes how many toothpicks we would need for any number of hexagons. Equation: ______________________________________________________

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1)2)3) 4) Fill-in-table AND graph: Directions: Fill in the missing spaces in the below function tables. Then, write the equation that would allow one to solve for (y), given any number (x). (x)(y) -2-10 -5 00 1 2 xy =_______ (equation) Name: _______________________________________________ Date:_____/_____/__________ (x)(y) 03 15 27 4 5 xy= _______ (equation) (x)(y) 15 29 313 4 5 xy =_______ (equation) (x)(y) 12 25 38 4 5 xy =_______ (equation)

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