Function rules and Other Tight Math Stuff Mr

Function rules and Other Tight Math Stuff Mr Streety’s 7 th Grade Class l Writing function rules from tables l Writing tables from Function rules l Graphing Tables and Function rules l Writing Function Rules from Graphs

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

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

Apples and Bananas Function Rule As you know we start with the equation: l 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. l

Apples and Bananas l l l 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 l l l 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 l l l Now we have our new equation y=3 x+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 l 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. l 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. l Y=3 x+2 l First we can choose any values for x we want unless they are given to us. l

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

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

Tables from Function Rules l 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. l From the table to the left we make a graph l

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

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

Mrs. Robinson's Lawn l 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 l 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