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?

Guest Jul 24, 2017

#1**0 **

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 less equal 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?

heureka Jul 24, 2017