Function Machines and Rules

The video tutorial explains how to find the rule for a function machine using a vertical table. It begins with an introduction to function machines and their rules, followed by a discussion on patterns and common differences. The tutorial then details how function machines work, emphasizing the importance of testing multiple inputs and outputs. It introduces the use of vertical tables to identify rules, demonstrating with examples. Finally, it shows how to determine the rule for a function machine by testing hypotheses and verifying results.

What is the primary goal when working with a function machine?

• To find the input number

• To determine the rule applied

• To identify the output number

• To change the machine's design

Which of the following is an example of a pattern?

• 5, 10, 15, 25

• 3, 6, 9, 12

• 1, 2, 4, 8

• 7, 14, 21, 29

What should you do to verify the rule of a function machine?

• Use only one input and output

• Test multiple inputs and outputs

• Change the machine's rule

• Ignore the outputs

What is a common mistake when analyzing a function machine?

• Stopping at one input-output pair

• Using too many inputs

• Changing the rule frequently

• Ignoring the machine's design

What is the purpose of using a vertical table in function machines?

• To display only the outputs

• To list all possible inputs

• To organize inputs and outputs for rule finding

• To change the function machine's rule

In the example with inputs 7 and 8, what rule was determined?

• Divide by 4

• Add 3

• Multiply by 5

• Subtract 2

What was the rule found for the function machine with inputs 4 and 7?

• Divide by 2

• Subtract 5

• Multiply by 4

• Add 12

Why is it important to check the rule with multiple inputs?

• To ensure the rule is consistent

• To find new inputs

• To change the machine's design

• To ignore incorrect outputs

What does the vertical table help illustrate in a function machine?

• The machine's speed

• The growth pattern of outputs

• The machine's design

• The number of inputs

What is the final rule determined in the lesson's example?

• Multiply by 3

• Add 12

• Subtract 4

• Divide by 5