Question

The ordered pairs (1, 81), (2, 100), (3, 121), (4, 144), and (5, 169) represent a function. What is a rule that represents this function?

Answer 1

The ordered pairs (1, 81), (2, 100), (3, 121), (4, 144), and (5, 169) follow the rule where the value of 'x' in the next ordered pair is the previous value of x + 1 and the next value of y is equal the 2 times the previous value of y minus the value of 2nd previous, plus 2. So the next ordered pair is (6, 196), where y = 2(169) - 144 + 2 = 196.

Answer 2

81=9^2
100=10^2
121=11^2 ...

that tells you it will have the form of:
( some function of x)^2

what function gives
9 when x=1
10 when x=2
11 when x=3...?