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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 involves guessingand-checking Function Rule Try adding/multiplying the X by some number to see if you can get Y You can also try adding/subtracting after you multiply Function Rule We can see the equation will be Y = 3x +2 Function Rule The second method works in the X values are consecutive (ex. 1, 2, 3) If they are, we can take the difference of the Y values (ex. 5-2 = 3) That result will be to coefficient for X (ex. Y = 3x) Now we will determine if we have to add/subtract a constant Mrs. Vanderbilt's Lawn We have been hired to mow Mrs. Vanderbilt'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. Vanderbilt'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. Vanderbilt's Lawn Mowing Lawns y-axis (dollars) Of course this is just the first two sets of numbers. Let’s see what happens if we plot the rest of the numbers 16 12 8 4 0 0 1 2 3 x-axis (hours) 4 5 Mrs. Vanderbilt'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. Mowing Lawns y-axis (dollars) 16 12 8 4 0 0 1 2 3 x-axis (hours) 4 5 Mrs. Vanderbilt'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 Mowing Lawns y-axis (dollars) 16 12 8 4 0 0 1 2 3 x-axis (hours) 4 5