Consider the following functions.f1(n) = (log n)2023f2(n) = n2logn(nn)f3(n) = n3+ 7n2f4(n) = 2. 023nf5(n) = n log nf6(n) = n *3n2Now do the followings:a. Write a correct asymptotic upper bound for each of the above.b. Sort the functions in ascending order of their growth rate, assuming n is significantlylarge. Just write the sorted order, no need to show any simulation.

Which of the given options provides the increasing order of complexity of functions f1, f2, f3 and f4:f1(n) = 2^nf2(n) = n^(3/2)f3(n) = nLognf4(n) = n^(Logn)

For each of the following pairs of functions, indicate whether the first functionof each of the following pairs has a lower, same, or higher order of growth (towithin a constant multiple) than the second function.a. n(n + 1) and 2000n2 b. 100n2 and 0.01n3c. log 2 n and ln n d. log 22 n and log 2 n2e. 2n−1 and 2n f. (n − 1)! and n!

5. Arrange the functionsn , 1000 log n, n log n, 2n!, 2n, 3n, and n2/1,000,000 in a list sothat each function is big-O of the next function.

able 2.1 contains values of several functions that often arise in the analysisof algorithms. These values certainly suggest that the functionslog n, n, n log 2 n, n2, n3, 2n , n!are listed in increasing order of their order of growth. Do these valuesprove this fact with mathematical certainty?b. Prove that the functions are indeed listed in increasing order of their orderof growth.

Which of the following time complexities indicates the slowest growing function?O(n!)O(2^n)O(n^3)O(n log n)