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

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

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

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.

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

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

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

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?

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.

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

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

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

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

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

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

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.

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