Expert: Robi Bhattacharjee - 2/22/2009

Question
Hello,
I am a 6th grade student and cannot solve this math equation and would like your help. Thanks

        Find the rule for the function table
            Input(x)           Output
               -2                 -2
               -1                  0
                2                  6
                3                  8


Answer
Hey Matt,

For this kind of question, there is no definite way of doing it. Sometimes you just see the pattern, and sometimes you don't. However, there are techniques that can help you discover the pattern.

One such technique is to look at the differences of outputs. Let me show you.

Your inputs are -2,-1,2,3

and your outputs are -2, 0, 6, 8

So when your input goes from -2 to -1 it goes up by 1

The corresponding outputs; -2 , 0 goes up by 2

So we can make a table of values.

If input goes up by 1 you go up by 2

up by 3 then up by 6

by 1 then up by 2

So now the pattern becomes obvious. If you go up from and input by a certain number, then the output goes up by twice as much.

So then, since you have the point an input of 2 and an output of 6, if the input is x, then your out put is 6 + 2(x-2) or it equals

6 + 2x - 4 which = 2x + 2.

Now you can try this out. 2(-2) + 2 = -2 which is the given output.

So your answer is output = 2(input) + 2


I hope this helps,
Robi