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Solutions for Session 3, Homework
See solutions for Problems: H2 | H3 | H4 | H5 | H6| H7
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Problem H2 | |
a. | Yes, the output is always Π, but there is exactly one output for any input. |
b. | No, the same team can have lots of different members. |
c. | No, the same CD can have many different songs. |
<< back to Problem H2
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Problem H3 | |
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Gabriela is correct. The number of matching outputs is not important (witness the "3" function!), only that there is exactly one output each time.
<< back to Problem H3
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Problem H4 | |
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The outputs are -8, -4, -2, -1, and -1/2. The iterates get closer and closer to zero.
<< back to Problem H4
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Problem H5 | |
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No matter what you start with, the inputs will get closer and closer to 1/2.
<< back to Problem H5
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Problem H6 | |
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In each case, the output value must equal the input, so writing the rule and making it equal n is one way to solve the problem.
a. | The fixed point is x = 1/2. |
b. | The fixed point is x = 9. |
c. | There is no fixed point. |
d. | There are two fixed points, x = 0 and x = 1. |
e. | The fixed point is x = 4. |
f. | There are two fixed points, x = 3 and x = -2. |
<< back to Problem H6
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Problem H7 | |
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Each output is three half-sized copies of the input, with a hole in the middle. The pattern can repeat itself indefinitely.
<< back to Problem H7
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