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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 > 4f(x,y) = (x - 4,y). If x \le 4 but y > 4f(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 fto that point and then moves to f(x,y). If the robot runs forever, how many different points will it visit?  ...Sorry for the long question

 Nov 11, 2014

Best Answer 

 #1
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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 > 4f(x,y) = (x - 4,y). If x \le 4 but y > 4f(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 fto that point and then moves to f(x,y). If the robot runs forever, how many different points will it visit?  ...Sorry for the long question

(1,1) → (6, 7) → (2, 7) → (2, 3) → (7, 9) → ( 3, 9) → (3, 5) → (3, 1) → (8, 7) → (4, 7) → (4, 3) → (9, 9) →

(5, 9) → (1, 9) → (1, 5) → (1, 1)

15 points...and the cycle starts over......

 

 Nov 11, 2014
 #1
avatar+130511 
+5
Best Answer

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 > 4f(x,y) = (x - 4,y). If x \le 4 but y > 4f(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 fto that point and then moves to f(x,y). If the robot runs forever, how many different points will it visit?  ...Sorry for the long question

(1,1) → (6, 7) → (2, 7) → (2, 3) → (7, 9) → ( 3, 9) → (3, 5) → (3, 1) → (8, 7) → (4, 7) → (4, 3) → (9, 9) →

(5, 9) → (1, 9) → (1, 5) → (1, 1)

15 points...and the cycle starts over......

 

CPhill Nov 11, 2014

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