This problem is tricky because it requires some intuition of "what to look for" when you're deciding on a function to represent the ordered pairs.
When the problem says "Ordered pair" it's saying that when it gives you 2 numbers, for example (0,1), it is a concise way of saying that when one number, x, is 0, another number, call it y, will be 1. x an y are related. When x changes it will cause a change in y.
We can use a function to represent that relationship. for example y = f(x).
y = f(x) is a way of writing a lot of different kinds of relationships, but here are a couple examples
f(x) = 2*x+6
f(x) = x-3
f(x) = x^3
Now, for this problem it's asking us to find a function f(x) where f(x) = y, so
f(the first number) = (the second number)
f(-2) = 1/16
f(-1) = 1/4
f(0) = 1
f(1) = 4
f(2) = 16
The first thing I notice is that we see 4 and 16 in here twice, so they may be important. 4 and 16 are related because 4 squared (4*4) is 16.
Similarly (1/4) squared (1/4*1/4) is 1/16
so when x goes from 1 to 2, y goes from 4 to 16 (gets squared)
when x goes from -1 to -2 y goes from 1/4 to 1/16 (gets squared)
Also, if you take 4 to the power of negative 1, it is equivalent to 1/4. (4^(-1)=4)
So, every "y" value is some power of 4.
1/16 is 4^-2
1/4 is 4^-1
1 is 4^0
4 is 4^1
16 is 4^2
Now, if you look at the values of the exponents (the rightmost number in the above expressions) we can see that generally y has the form 4^x. So, we can write
y = f(x) = 4^x
