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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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Session 3, Part C:
Function Machines

In This Part: About Function Machines | Running a Function Machine | Function Machines and Undoing

The connected machine is really a single function that takes an input, runs it through the network inside, and produces an output.

This activity will allow you to control a network of function machines. You control the input and the operation performed by each function machine. Use the activity to help you answer Problems C1-C5.

This activity requires the Flash plug-in, which you can download for free from Macromedia's Web site. If you prefer, you can view the low-tech version of this activity, which doesn't require the Flash plug-in.

Use the Interactive Activity to try this algorithm, which we'll call Algorithm C. (If you need help using the machine, look at the sample.)

• 

Pick a number (that's the input)

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Multiply it by 2

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Add 3 to the answer

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Multiply that answer by 10

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Add 6

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Finally, divide by 2

Problem C1

Solution  

If the input to Algorithm C is 3, what is the output?

 

Problem C2

Solution  

If the output to Algorithm C is 88, can you determine what the input was? How did you do it?

 

Problem C3

Solution  

Use the Interactive Activity to build Algorithm D, which undoes Algorithm C. How would this help with Problem C2?

 

Problem C4

Solution  

Imagine that Algorithm C and Algorithm D are connected to form one large network. What would happen to a number used as an input in this network? Think about it for a few minutes, and try a few numbers if you need to.

Stop! Do the above problem before you proceed. Use the tip text to help you solve the problem if you get stuck.
Connecting the two networks gets you back to your original number. Going through all these steps turns out to be a complicated way of doing nothing to a number!   Close Tip

Take it Further

Problem C5

 Solution  

 

See if you can use the function machines in the Interactive Activity to produce the following outputs: 59, 216, 15625, 7280, 0.12345. As an additional challenge, use the fewest possible machines to do so.

 

Next > Part C (Continued): Function Machines and Undoing

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