;; The first three lines of this file were inserted by DrScheme. They record metadata
;; about the language level of this file in a form that our tools can easily process.
#reader(lib "htdp-beginner-reader.ss" "lang")((modname 11.2.1) (read-case-sensitive #t) (teachpacks ((lib "draw.ss" "teachpack" "htdp") (lib "arrow.ss" "teachpack" "htdp"))) (htdp-settings #(#t constructor repeating-decimal #f #t none #f ((lib "draw.ss" "teachpack" "htdp") (lib "arrow.ss" "teachpack" "htdp")))))
;A natural-number is
;1. 0 or
;2. (add1 n) where n is a natural-number.
;
;A list-of-symbols is
;1. an empty list or
;2. (cons s los) where s is a symbol and
;los is a list-of-symbols.
;
;repeat : natural-number symbol -> list-of-symbols
;Given a natural-number n, returns word n times
;as a list-of-symbols.
;
;Template
;(define (repeat n word)
;  (cond
;    [(zero? n) ...]
;    [else ... (repeat (sub1 n)) ...]))

(define (repeat n word)
  (cond
    [(zero? n) empty]
    [else (cons word (repeat (sub1 n) word))]))

;; f : number  ->  number
(define (f x)
  (+ (* 3 (* x x)) 
     (+ (* -6 x)
        -1)))
;
;A list-of-posns is either
;1. an empty list or
;2. (cons p lop) where p is a posn and lop is a list-of-posns.
;tabulate-f : natural-number -> list-of-posns
;Creates a "table".  Returns a list of n posns of the form
;(cons (make-posn (f n) n) (cons (make-posn (f (- n 1) (- n 1)))...

(define (tabulate-f n)
  (cond
    [(zero? n) empty]
    [else (cons (make-posn (f n) n) (tabulate-f (sub1 n)))]))