Function Machines and Algebraic Relationships

The video tutorial explores number patterns, focusing on function machines and tables. It explains how to identify rules in function machines, using addition and multiplication, and how to analyze patterns in tables. The tutorial also covers subtraction in function machines, providing strategies to determine the rules governing input-output relationships.

What is a function machine in the context of number patterns?

• A device that multiplies numbers by 10

• A tool for measuring the size of numbers

• A concept that transforms input numbers using a specific rule

• A machine that divides numbers by 2

In a function machine, if the input is 4 and the output is 20, what could be the rule?

• Subtract 4

• Multiply by 5

• Divide by 2

• Add 16

If a function machine adds 16 to each input, what will be the output for an input of 14?

• 30

• 32

• 34

• 28

Why is it important to check multiple inputs in a function machine?

• To ensure the rule is consistent

• To find the largest output

• To make the machine faster

• To reduce the number of inputs

In a table showing ticket costs, if 1 ticket costs $15, what is the cost for 6 tickets?

• $100

• $75

• $80

• $90

How can you represent the relationship between tickets and cost using an algebraic equation?

• t + 15 = c

• t - 15 = c

• t * 15 = c

• t / 15 = c

In a function machine where the input is 15 and the output is 6, what is the rule?

• Add 9

• Subtract 9

• Divide by 3

• Multiply by 2