I.a) For the following functions, visualize the functions for n {1,2,4,8,16,32,64,128,256,512,1024}

1) lg₂n

2)

3) n

4) n*lg n

5) n^2

6) n^3

7) 2^n

8) n!

I.b) Find the range of n (input) such that merge sort outperforms insertion sort in the worst-case scenario.

I.c) Find the range of n (input) such that insertion sort outperforms merge sort in the average-case scenario.

I.d) Find the range of n (input) such that bubble sort outperforms selection sort in the best-case scenario.