USE DrRACKET to write for following functions

1.rotate: takes an integer n 0 and a list and "rotates" n elements off the front of the list onto the end.

E.g., > (rotate 3 '(1 2 3 4 5 6 7 8 9)) '(4 5 6 7 8 9 1 2 3)

2.lookup: treats a list of pairs as a lookup structure (aka "associative list"); when given a key and a list, it finds the pair whose car matches the key (using equal?) and returns the associated cdr. If no match exists, returns #f.

E.g., > (lookup 'a '((a . apple) (b . bee) (c . cat))) 'apple

> (lookup 'foo '((a . apple) (2 . "two")))

#f

3. update: updates or inserts a new pair into a lookup list (as used by lookup) reflecting a provided key/value mapping. (The location of a newly inserted pair doesn't matter.)

E.g.,> (update 'a 'apple '((b . bee) (c . cat))) '((b . bee) (c . cat) (a . apple))

4.equal-shape?: returns #t if two pairs have the same "shape", i.e., if their structure consisting of zero or more nested pairs is identical; returns #f otherwise.

E.g., > (equal-shape? '(1 2 3) '(2 3 4)) #t