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Patterns, Functions, and Algebra
 
Session 8 Part A Part B Part C Homework
 
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Session 8:
Homework

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).

function machine

Problem H1

Solution  

If the input is 5, what is the output?


 

Problem H2

Solution  

If the input is 12, what is the output?


 

Problem H3

Solution  

If the input is 2, what is the output?


 

Problem H4

Solution  

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?


 

Problem H5

Solution  

Make an input/output table for this function. What kind of function is it?


Take it Further

Problem H6

Solution

Make a list of all the numbers that leave a remainder of 3 when divided by 5 and a remainder of 1 when divided by 3, then give one rule that would find them all.


Problem H7

Solution

If my age is divided by 3, the remainder is 2. If my age is divided by 5, the remainder is also 2. If my age is divided by 7, the remainder is 5. How old am I?


Problem H8

Here's a table showing the first two outputs for the linear function y = 3x - 2. Come up with at least two other functions that match these outputs, and complete the table using your functions.

x

3x-2

Your
function

Your
function

1

1

1

1

2

4

4

4

3

4

5

show answers
 
 

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