Scheme Homework #2

Create the functions below in the upper (definitions) pane of DrRacket, save to a file and upload the file to the Homework server.

1. Create the function:

f(x) is 2 when x <= 3, and is x² - 3x + 8 when x > 3 

Put the test cases (and their correct answers) that you'll be using to test this function into the Comments-to-Teacher.

2. Create a function called Div23 which is given an integer (non-negative) and returns #t if it's evenly divisible by either 2 or 3 or both, and #f if neither.  Examples:

	(div23 3) ; -> #t
	(div23 8) ; -> #t
	(div23 6) ; -> #t
	(div23 35) ;-> #f

3. Create the function:

fred(me):
    0 if  me < 0
    5 if me >= 0 and me is evenly divisible by 5
    23 otherwise

4. We want to convert from ordinary 12-hour time, to Navy time (24-hour time).  For instance, 3 AM would be converted to just 3, and 11 AM would be just 11.  But 2 PM would be 14, and 11 PM would be 23.  But be careful: 12AM (namely, midnight) would be 0 in Navy time and 12PM (noon) would be 12.  Create a function called ToNavyTime(hour,ampm) that takes 2 arguments, the first argument is the ordinary (clock) hour, and the second argument is 0 if it's AM, and 1 if it's PM.  The function returns the Navy time.

(ToNavyTime 11 0) ; -> 11 (which is 11 AM)
(ToNavyTime 1 1)  ; -> 13 (which is 1 PM)
(ToNavyTime 12 0) ; -> 0  (which is midnight)
(ToNavyTime 12 1) ; -> 12 (which is noon)

5. Challenge Problem:  Create the definition for the same function ToNavyTime(hour,ampm) as above, but without using IF or COND.  Use only the built-in Scheme functions that you know.

6. Challenge Problem: Create the function SmallestDivisor(N) which will be given a composite (non-prime) integer between 2 and 100, and will return the smallest divisor of that integer (greater than 1).