A B C D EHomework

Solutions for Session 3, Homework

See solutions for Problems: H2 | H3 | H4 | H5 | H6| H7

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.

 Problem H3 Gabriela is correct. The number of matching outputs is not important (witness the "3" function!), only that there is exactly one output each time.

 Problem H4 The outputs are -8, -4, -2, -1, and -1/2. The iterates get closer and closer to zero.

 Problem H5 No matter what you start with, the inputs will get closer and closer to 1/2.

Problem H6

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.

 Problem H7 Each output is three half-sized copies of the input, with a hole in the middle. The pattern can repeat itself indefinitely.

 Session 3: Index | Notes | Solutions | Video