1) [20 pts] For the following functions, visualize the functions for n{1,2,4,8,16,32,64,128,256,512,1024} I. lg2n II. n III. n IV. n.lgn V. n2 VI. n3 VII. 2n VIII. n ! 2) [30 pts] Find the range of n (input) such that merge sort outperforms insertion sort in the worst-case scenario. 3) [30 pts] Find the range of n (input) such that insertion sort outperforms merge sort in the average-case scenario. 4) [20 pts] Find the range of n (input) such that bubble sort outperforms selection sort in the best-case scenario