Function Tables Today’s Lesson: What: Why: . . . so I can represent function tables as equations and as graphs

Describe the relationship between tables, graphs, and equations.

Describe the “magic number” rule in your own words.

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

Sometimes it is helpful to think of a Function table as an input/output “Machine” . . . As the inputs (x values) and outputs (y values) are revealed, can you figure out the “machine rule”? 1) Input (x) Output (y) Rule: Equation: “plus 3” y = x + 3 3 1 4 2 5 3 6 4 7 50 53

Sometimes it is helpful to think of a Function table as an input/output “Machine” . . . As the inputs (x values) and outputs (y values) are revealed, can you figure out the “machine rule”? 2) Input (x) Output (y) 1 4 2 7 3 10 5 Rule: Equation: “times 3, plus 1” y = 3x +1 13 16 100 301

Every input/output is an ordered pair, so it is easy to graph . . . 3) Rule: Equation: “times 2, minus 1” Input (x) Output (y) 1 2 3 5 4 y = 2x -1 40 7 79 9 Every input/output is an ordered pair, so it is easy to graph . . . Notice the straight line. We will be studying linear functions during this unit. They will ALL graph as a straight line!

Yes . . . I call it The “magic number” shortcut . . . 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 ! (x) (y) 1 4 2 6 3 8 5 There is a +2 pattern going down the y column . . . 10 12 Step Two: The magic number tells you what to multiply x by! Our magic # is __________ . 2 So, the first part of the equation is 2x . . . Step Three: See if you need a second step . . . When we multiply our “x” numbers by 2, we see what we still need to add 2 in order to equal “y.” Final Equation: y = 2x + 2 Catch– the “magic” only works if your inputs are in a row!!

Let’s tie it all together (use the shortcut to help You) . . . 1) Table: Equation: Graph: (x) (y) -2 1 2 4 3 y = 3x - 2 7 + 3 pattern . . . 10

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

Your turn . . . This is a subtraction pattern going down “y.” This means the magic # is negative! 3) Table: Equation: Graph: (x) (y) -3 10 -2 6 -1 2 1 y = -4x - 2 -2 - 4 pattern . . . -6

Wrap it up/Summary: Describe the relationship between tables, graphs, and equations: Describe the “magic number” rule in your own words: They are different ways of representing the same function. Also… You can use a table to make a graph. You can use an table to write an equation. Look at the “y” column. See what number is being added. This is the MAGIC NUMBER! The magic number is the number being multiplied by “x”. Next, check to see if you need to add anything!

END OF LESSON