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Session 8:
Homework
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We said previously that algebra has become very much concerned with operations. So far, the only operations we've used are the ones from arithmetic. Let's take a quick look at another kind of operation that often shows up in algebra. Consider the operation that divides a whole number by 3 and hands you back the remainder. This is usually called the "mod 3" operation.
Example: 17 divided by 3 is 5 with a remainder of 2, so we say 17 mod 3 = 2, or 17 = 2 (mod 3).
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Problem H1 |  |
If the input is 5, what is the output?
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Problem H2 | |
If the input is 12, what is the output?
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Problem H3 | |
If the input is 2, what is the output? |
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Problem H4 | |
Now try some undoing:
a. | Describe all the numbers that produce an output of 1. |
b. | What is the "pullback" of 2? (The pullback of an output is the collection of inputs that produce it.) |
c. | What numbers produce an output of zero? |
d. | How many possible outputs are there for this function? What are they? |
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Problem H5 | |
Make an input/output table for this function. What kind of function is it? |
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