Variables using

input output
  1 ->  3 
  2 ->  5
  3 ->  9
  4 -> 17
  5 -> 33

How do you get the answer?

To solve it we must be clever enough to observe
a pattern. 

Notice by looking at the row of five numbers:

 3,  5,  9, 17, 33

that they are respectively 1 more than this
row of five numbers:

 2,  4,  8, 16, 32

If we are clever enough, we can recognize the 
row of five numbers above as the successive 
powers of 2:

21, 22, 23, 24, 25 

So the rule for the function is 

"Take the input number, raise 2 to that power, add one 
to that and the number you get will be the output number."

If each input is represented by a value of x and
each output is represented by a value of y, then
 
            y = 2x + 1

This can also be represented by f(x) instead of y, like
this

         f(x) = 2x + 1         

Edwin