Homework 1

Due Date: Friday September 18, 6pm

Purpose To write simple functions.

Expectations

• All Finger Exercises on this homework should be done individually (without a partner) and you should have them done by Monday night. Finger exercises will not be graded and do not have to be turned in.

• All Graded Exercises on this homework should be done with the partner you're assigned in lab on Tuesday Sept 15.

• For this and all future assignments you must submit a single .rkt file containing your responses to all exercises via the Handin Server. We accept no email submissions.

• You must use the language specified at the top of this page.

• On this assignment, you are encouraged to write signatures and purpose statements for every function you write, in the format we studied in class; we will give you feedback on how clear or accurate they are. On future homeworks, they will be required and graded as part of the assignment. As for check-expects: follow the individual instructions for each problem.

Failure to comply with these expectations will result in deductions and possibly a 0 score.

Finger Exercises You are not required to submit your finger exercises but they will be helpful so we recommend doing them anyway.

Exercise 1 Write a function that subtracts 2 from a number.

Exercise 2 The following table describes how far a person has gone in a race in a certain amount of seconds:

t =		1		2		3		4		5		6		7		8		9		10
d =		3		4.5		6.0		7.5		9.0		10.5		12.0		13.5		?		?

Write a function that predicts, based on this data, how far they will have run at time t. Write three check-expects: two that test to see the data in the table matches your function’s output, and then one more that tests the output when t is at least 9.

Exercise 3 Take a look at figure 1, which is a graph of f, a function of x.

Turn the graph into a table for x = 0, 1, 2 and 3 and formulate a function definition.

Figure 1: A function graph for f

Exercise 4 Translate the following mathematical function into a BSL function:

f(x) = x2 + 12

Use it to create a table for x = 0, 2, 5, and 9.

Exercise 5 Enter the following function definition in BSL into DrRacket:

(define (math-is-boring x)

(+ (* -4 (expt x 3)) (* 8 (expt x 1)) (* 9 (expt x 0))))

Look up the documentation for expt.

Apply the function to 0, 1, and 3 in the interactions area.

Apply the function to 1 in the definitions area and use the stepper to see how DrRacket evaluates this program.

Exercise 6 Enter the following function definition in BSL into DrRacket:

(define (hello x)

(cond

[(string=? "Ben" x) (string-append "Dear " x ", Esquire:")]

[(string=? "Leena" x) (string-append "Dear " x ", Esquirette:")]

[else (string-append "Greetings, " x ", ")]))

What kind of argument does hello consume? Apply the function to your favorite argument and step through the evaluation.

Exercise 8 Write a function, nineply, that multiplies a number, supplied as an argument, by 9. Write three check-expects: one for a negative value, another for zero, and a third for a positive value.

Exercise 9 Complete the following table:

t =		0		1		2		3		4		5		6		7
d =		FUNDIES		FUNDIE		FUNDI		FUND		FUN		FU		?		?

Turn this table into a function definition. In a comment before the function, give as precise a signature for this function as you can (hint: it’s not quite straightforward – you may need to describe it rather than use the notation from class).

Exercise 10 Implement the function, cycle-spelling, so that when (animate cycle-spelling) is called, it animates spelling the following long word, letter-by-letter (in all caps). When the end of the word is reached, it cycles back and starts from the beginning.

(define LONG-WORD "diScomBoBUlaTeDiScomBoBulaTeDboBUlaTeD")

The word should be displayed in blue in font size 40 on a white background.

Hints:

• Your code ought to work no matter what string is used when defining LONG-WORD, without needing to change anything else.

• One way to count 0 up to some number and then loop back is to think about dividing two numbers and taking the remainder; so the remainder of 1 / 3 is 1, the remainder of 2 / 3 is 2; and the remainder of 3 / 3 is back to 0. Look for the remainder function in BSL.

• You may want to look at the documentation at https://docs.racket-lang.org/htdp-langs/beginner.html for some of the functions available to you in BSL.

Exercise 11 Design a function, draw-kite, that produces a kite with 4 colors when given the desired width and height of the kite. We have provided two check-expects to help you test your function in the starter file for this assignment.

• The kite should have the following four colors, starting with the top left quadrant going clockwise: "blue", "yellow", "green", "red".

• The widest point of the kite is at one-third of the distance from the top and two-thirds from the bottom.

Exercise 12 Write a function, convert-to-inches, that takes as arguments a number of yards, feet, and inches (in that order) and converts to a total number of inches. For example, (convert-to-inches 4 1 6) would produce 162 inches. Write two check-expects: one expressing the example above, and a different one of your choosing.

Exercise 13 Design the function speed-check. It consumes two natural numbers: one that represents the speed of a car and the other one the speed limit of the road. The result is one of these strings: (1) "okay" for a car that goes below the speed limit; (2) "bit fast" for a car that is going at most 9 mph faster than the speed limit; or (3) "speeding: ___ mph over limit" for a car that exceeds the speed limit, where the underlines are replaced by how much the car is over the speed limit. Write five check-expects that test the function’s behavior in different scenarios.