Finding Function Rules

Use input/output tables or graphs to find function rules

We will be finding function rules to find and graph answers to linear equations

Firs you must find out two facts about the function you are examining. You must find the change in y and the starting point for the function

The first step when using an input/output table is finding the change in y values when the change in x is 1. Typically we want to see our input x values starting at 0 and increasing by 1 each step.

So if we have the following values x y

0 3

1 7

2 11

We can see that as x increases by 1, y increases by 4.


Now that we have this element we want to look at what the y-value is when x is zero.

In our example the y-value is 3

So our change in y is 4, and our starting point is 3

Now we need to put these elements together to create our function rule.

Creating our function

First we need to know what to do with our starting point of 3 and our change in y of 4. The change in y is the coefficient for x, and then we add our starting point. The form that we want our equation to be in is:

y=mx+b

Where m is the change in y, and b is the starting point.

In our example our equation will look like:

y=4x=3



Now try when the change in y is 8 and the starting point is 27.




WATCH THE VIDEO BELOW FOR STEP-BY-STEP INSTRUCTIONS ON HOW TO FIND A FUNCTION USING TWO POINTS IN AN INPUT AND OUTPUT TABLE

Ex: Find the Linear Function Given Two Function Values in Function Notation