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**Function rules and Other Tight Math Stuff Mr Streety’s 7th Grade Class**

Writing function rules from tables Writing tables from Function rules Graphing Tables and Function rules Writing Function Rules from Graphs

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**Function Rules from Tables**

There are two ways to write a function rule for a table The first is through number sense. This is the Harder of the two

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**Function rules from tables**

When X=0, what does Y=?. This gives you the first part of your function y=x+2 After you find what Y= when X=0, you need to subtract this number from the following values for Y

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**Apples and Bananas Function Rule**

As you know we start with the equation: y=Ax+B Where A and B are constant numbers, and of course x and y are variables meaning their value changes with the table.

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Apples and Bananas The first step here is to solve for B, using the first set of numbers from the table y=Ax+B 2=A(0)+B B=2 This gives us the new equation y=Ax+2

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**Apples and Bananas Function Rule**

The second step is to use our new equation to find a value for A Y=Ax+2 5=A(1)+2 5-2=A(1)+2-2 3=A(1) A=3

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**Apples and Bananas Function Rule**

Now we have our new equation y=3x+2 We can plug our x values in to check the equation y=3(2)+2 Y=6+2 Y=8

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Mrs. Robinson's Lawn We have been hired to mow Mrs. Robinson's lawn. She is going to give us a two dollar bonus for starting early. In addition to this she will pay us 3 dollars an hour. What is the function rule for this problem?

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**Writing Tables from Function Rules**

Since 2 dollars is a bonus, we get that as soon as we start. We get 3 dollars an hour after that. Y=3x+2 First we can choose any values for x we want unless they are given to us.

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**Tables From Function Rules**

The next step is to plug these values in for the variable x in our equation. Y=3x+2 Y=3(0)+2 Y=2

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**Tables From Function Rules**

Now let’s try the next set of numbers. y=3(1)+2 y=5

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**Tables from Function Rules**

As you plug in the rest of the values for x, you will get the corresponding values for y.

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**Graphing Tables and Function Rules**

First of all if you only have a function rule you need to make a table which we just covered. From the table to the left we make a graph

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Mrs. Robinson's Lawn We will need to plot the set of numbers as they as they appear in the table. For the first set of numbers we will go 0 to the right and up 2 For the next set of numbers we will go 1 to the right and 5 up

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Mrs. Robinson's Lawn Of course this is just the first two sets of numbers. Let’s see what happens if we plot the rest of the numbers

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Mrs. Robinson's Lawn After plotting all the points we can draw a line from point to point that will help us find values between the points.

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Mrs. Robinson's Lawn Using the line we can tell how much money we can make mowing her lawn for 2 and a half hours or or four and a half

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