If the robot runs forever, how many different points will it visit?

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 $x \le 4$ 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?

asked May 31, 2016 in ALGEBRA 2 by anonymous
reshown May 31, 2016 by goushi

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If the robot runs forever, how many different points will it visit?

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