writing a rule

Question

how do i write a rule for the following functions

 

______________________________

 

x          -1        0           1               2

 

y           3         1          1/3          1/9

 

 

I think x you are adding by one   and y you are dividing by 3.

Answer 1

It depends on whether you're trying to find a relationship between x and y, or for each function, x, and y, separately.  y = (1/3)^x is correct for the former.  

For the latter, you would have  iterative functions, where the next term (i) in the series depends on the previous one (i-1) in the following manner:

x_i = x_i-1 + 1  and y_i = y_i-1/3

Answer 2

 

 

 

y = (1/3)^x