f(2)=1100, f(5)=2450, f(8)=3800, f(x) = ?

This appears to be linear......

Consider the slope between the first two points and then between the second and third points:

(2450 - 1100)/ (5-2) = 450      and

(3800 - 2450) / (8-5)  = 450

So the slope is the same, indicating a linear function.

Now, we can find the "y intercept" (where x = 0) by noting that everytime x changes by 1, y changes by 450. So when x changes from 2 to 0, y decreases from 1100 by (2 * 450) = 900. So 1100 - 900 = 200.

And the equation of our line is

y = 450x + 200