1. Big-O notation. We have learnt big-O notation to compare the growth rates of func- tions, this exercise helps you to better understand its definition and properties. (a) (10 points) Suppose n is the input size, we have the following commonly seen functions in complexity analysis: fi(n) = 1, f2(n) = logn, f3(n) = n, fA(n) = nlogn, fs(n) = n2, fo(n) = 2". Intuitively, the growth rate of the functions sat- isfy 1