Originally Posted by

**tabularasa** Hi, Im not sure wether this question is under right area.

I have a problem, in a field on numeric analysis. I'm trying to understand pragmatically interpolation and extrapolation and other techniques related to approximation.

Suppose my measure device has logged two data which are related each other, I call the data as x and y.

logged data:

x: {1,3,5,8,25,33}

y: {4,16,36,81,676,1156}

Ok, now I have to somehow approximate a function to calculate (approximate) values inside x-area and outside x-area.

For example, what is value of y when x = 4 and when x = 101.

How the interpolation and extrapolation works in this case and if there is a general function f(x). And how to get that function from measured points?

Could you math pros help me on this?