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 x4, f(x,y)=(x-4,y). If x4, 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?

Question

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?

Steve · Answer

that would be the plan. Should be pretty straightforward. One you get back to (1,1) you're done.