8. Number Finale

We are going to make this graph:

The equation we are using is:

(define (func x)
  (* (- x 5)
     (+ x 2)
     (- x 7)))

The range of people coordinates we want to graph is: $$-5 \le x \le 7 $$ $$-400 \le y \le 100 $$

Your want to make the graph have dimensions 360x250 (in computer coordinates).

1. Write two checks for the function x-computer->x-people that takes in a computer coordinate and puts out a people coordinate.

2. Possibly using WolframAlpha, write the function x-computer->x-people.

3. Write two checks for the function y-people->y-computer.

4. Write and test the function y-people->y-computer.

5. Check your work.

   (check-expect (x-computer->x-people 150) 0)
   (check-expect (y-people->y-computer 0) 50)

6. Write a draw handler that will place a dot on the graph of the function. The model will be the computer x-coordinate.

7. Design and test a tick handler that will start on the left side of the screen, trace the curve to the right side, then repeat.

Bonus: Graph of the line

1. Write rf (or real-func), which takes in a computer x-coordinate, changes it to people x-coordinates, applies your function, and then changes the result back to computer y-coordinates. You may have already written this as part of your animation.

2. Use build-image to create a 360x250 image where the amount of gray at (x,y) is given by limiting $$ 100 * \left| y - \text{rf}(x) \right| . $$

3. It took a little extra work to get the axes to show with this method…