Question

The ordered pairs ( 1 , 4 ) , ( 2 , 1 6 ) , ( 3 , 6 4 ) , ( 4 , 2 5 6 ) , ( 5 , 1 , 0 2 4 ) ( 1 , 4 ) , ( 2 , 1 6 ) , ( 3 , 6 4 ) , ( 4 , 2 5 6 ) , and ( 5 , 1 , 0 2 4 ) represent a function. What is a rule that represents this function?

Answer 1

The rule is f(x) = 2^(2x).

Explanation:

Note that 4 = 2^2, 16 = 4^2, 64 = 8^2, 256 = 16^2 and 1024 = 32^2

and the first numbers in the ordered pairs are 1 , 2 ,3, 4, 5

compare this with 2, 4 , 8, 16 , 32.

We see that the rule for this is 2^x where x is the sequence number.

So the rule for the original ordered pairs is (2^x)^2.

= 2^2x.