The function f(x,y) accepts an ordered pair as input and gives another ordered pair as output. It is defined according to the following rules: If x>4, f(x,y)=(x-4,y). If x<=4 but y>4, f(x,y)=(x,y-4). Otherwise, f(x,y)=(x+5,y+6). A robot starts by moving to the point (1,1). Every time it arrives at a point (x,y), it applies f to that point and then moves to f(x,y). If the robot runs forever, how many different points will it visit?
Would I just plug in 1,1 and then plug the results of that, and so on until you have repeat points?
that would be the plan. Should be pretty straightforward. One you get back to (1,1) you're done.
Yes, to determine the number of different points the robot will visit, you can start by plugging in the initial values (1,1) into the function f(x,y) to find the first point the robot will move to.
In this case, f(1,1) = (1+5, 1+6) = (6,7). So, the robot will move to the point (6,7).
Next, you can apply the function f(x,y) to (6,7) to find the next point the robot will move to.
Since x > 4 (6 > 4), the rule f(x,y) = (x-4, y) applies. Therefore, f(6,7) = (6-4,7) = (2,7). So, the robot will move to the point (2,7).
You can continue this process of applying the function f(x,y) to each subsequent point to find the next point the robot will move to. Keep track of each new point and check if the robot revisits a point it has already been to.
If the robot runs forever without revisiting any point, the number of different points it visits will be infinite. However, if it revisits a point, you can stop the process and count the total number of different points visited before the repetition occurred.