what is the rule if the input is 1 and output is 9 and input is 2 and output is 12 and the input is 3 and output 16

Answer 1

1 ---> 9
2 ---> 12
3 ---> 16

hard to tell, it is not linear,

I don't know what level this is,
let's assume it is a quadratic
I did some quick calculations and got
y = (1/2)x^2 + (3/2)x + 7
or
y = (x^2 + 3x + 14)/2

works for your 3 values