i looked at the 0's first. in the first problem, 0 --> 4. so i assume y = (some manipulation of x) + 4.
so then i subtracted 4 from all the other y-values, and tried to figure out what i would do to x to get them. i thought about multiplying by a negative number to make it positive, since all the negative numbers went to positive, but it did not work for all. so then i thought of squaring. and it worked!
same for the second. i saw 0 --> -1, so i thought y = f(x) - 1. after playing around a bit, 4x was the obvious choice
sorry i can't explain more, but i'm in a rush...
I'll do the easier one first . . .
Take the difference of consecutive values of
The first differences are constant.
. . Hence, the function is of the first degree (linear).
The general linear function is: .
Use any two values from the table to set up a system of equations.
Take consecutive differences, then the differences of the differences.
The second differences are constant.
. . Hence, the function is of the second degree (quadratic).
The general quadratic function is: .
Use any three values from the table to set up a system of equations.
Then  and  become: .
Add  and : .