5. A range function similar to the range function in Python. For example, range (2,12,3) returns the list [2,5,8,11], and range(20, 2, -3) yields [20, 17, 14, 11, 8, 5] 6. A slice function, with functionality similar to the Python list slice operator. For example, slice ([11,22,3,14,5,6], 1, 4) returns the list [22,3,14]. Assume that the indices specified are valid for the list. Hint: Write a helper function nthElement that returns the element at a specified (0-based) index in a list. For example, nthElement([10, 2, 34, 20], 2) returns 34, the element at index 2. 7. A binarySearch function that recursively implements the binary search algorithm to search a sorted integer list for a specified integer and returns true if it is found, false otherwise. For example, binarySearch ([100,200, 300, 400, 500], 200) returns true, whereas binary Search ([100,200, 300, 400, 500], 299) returns false. Hint: Write a helper function mid that returns a tuple (index, value) representing the middle value in a list. For example, mid [10, 2, 40, 8, 22] returns (2,40) because the value 40 at index 2 is the middle value in the list. Similarly, mid [10, 20] would return (1, 20). Use mid in conjunction with slice to implement binarySearch.