1. * Write an algorithm that counts the number of negative numbers in a given sequence of integers. 2. * Consider the sequence of integers: 1, 3, 5, 7, 9, 11, 13, 15. We want to find x = 11. Run 3 iterations of the binary search algorithm. What sequence remains? 3. * Consider the sequence of integers 12, 4, 7, 9, 6. (a) Apply the bubble sort algorithm to this sequence. Show all steps. (b) Apply the insert sort algorithm to this sequence. Show all steps. 4. * Determine orders of the functions below. Prove your answers. You may use any results from class. (a) f(x) = 4x2023 +58x0 (b) g(x) = x log(x8 + 7) +x5 +1