How to find the function rule from a table?

Question

I was trying to graph (1, 1)(2, 2)(3, 4)(4, 8)(5, 16)(6, 32)(7, 64)(8, 128)(9, 256)(10, 512) and I just couldn't do it. Does anyone know what the function rule of this is and how to find it in similar problems in the future?

Answer 1

Function rule of above is given by,

$$f(n)= 2^{n-1}$$

One finds rule by just observing the pattern. So keep trying many examples.