What Are the Rules For These Functions...?

Question

2----3----7----10
8----7----3-----0

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0----4----8---12
5----7----9---11

Answer 1

Let the top row be x and the bottom row y.

First problem: y = -x + 10
Second problem: y = (1/2)x + 5

Answer 2

For the second one:
0----4----8---12
5----7----9---11
Notice that 0, 4, 8, 12 are all multiples of 4.
We could say 4n
Notice that 5, 7, 9, 11 and consecutive odd numbers.
Odd numbers can be written as 2n+1
To correspond to 5, it would have to be 2n+5
f(4n) = 2n+5, for n = 0, 1, 2, and 3

Answer 3

what the 1st person said