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Learning Math Home
Patterns, Functions, and Algebra
 
Session 3 Part A Part B Part C Part D Part E Homework
 
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Algebra Site Map
Session 3 Materials:
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A B C D E
Homework

Video

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.

<< back to Problem H2


 

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.

<< back to Problem H3


 

Problem H4

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

<< back to Problem H4


 

Problem H5

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

<< back to Problem H5


 

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.

<< back to Problem H6


 

Problem H7

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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