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# 3.4: Function Machines 1

Difficulty Level: At Grade Created by: CK-12

Can you use the rule described in the picture below to finish the table? In this section, we will use rules, addition, and subtraction to complete function tables.

### Function Machines 1

In order to complete function tables like the one above, we can use the problem solving steps to help.

• First, describe what you see in the table.
• Second, identify what your job is. In these problems, your job will be to complete the table.
• Third, make a plan. In these problems, your plan should be to use the rule to help you to complete the table.
• Fourth, solve. In these problems you will solve by completing the table.
• Fifth, check. In these problems you will check by counting up or down to make sure that you completed the table correctly.

1. Follow the rule. Complete the table.

We can use the problem solving steps to help us solve this problem.

\begin{align*}& \mathbf{Describe:} && \text{The table has} \ \mathbf{IN} \ \text{numbers and} \ \mathbf{OUT}\\ &&& \text{numbers. Some OUT numbers are missing. The rule says add 1.}\\ & \mathbf{My \ Job:} && \text{Fill in the other OUT numbers.}\\ & \mathbf{Plan:} && \text{Add} \ 1 \ \text{to each} \ \mathbf{IN} \ \text{number to get the} \ \mathbf{OUT} \ \text{number.}\\ & \mathbf{Solve:}\end{align*}

In Out
2 3
6 7
0 1
8 9
4 5

\begin{align*}& \mathbf{Check:} && \text{Start with the IN number. Count up:} \ 6, 7\\ &&& \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ 0, 1\\ &&& \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ 8, 9\\ &&& \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ 4, 5\end{align*}

2. Follow the rule. Complete the table.

We can use the problem solving steps to help us solve this problem.

\begin{align*}& \mathbf{Describe:} && \text{The table has} \ \mathbf{IN} \ \text{numbers and} \ \mathbf{OUT}\\ &&& \text{numbers. Some OUT numbers are missing. The rule says add 3.}\\ & \mathbf{My \ Job:} && \text{Fill in the other OUT numbers.}\\ & \mathbf{Plan:} && \text{Add} \ 3 \ \text{to each} \ \mathbf{IN} \ \text{number to get the} \ \mathbf{OUT} \ \text{number.}\\ & \mathbf{Solve:}\end{align*}

In Out
4 7
5 8
1 4
2 5
7 10

\begin{align*}& \mathbf{Check:} && \text{Start with the IN number. Count up:} \ 5, 6, 7, 8\\ &&& \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ 1, 2, 3, 4\\ &&& \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ 2, 3, 4, 5\\ &&& \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ 7, 8, 9, 10\end{align*}

3. Follow the rule. Complete the table.

We can use the problem solving steps to help us solve this problem.

\begin{align*}& \mathbf{Describe:} && \text{The table has} \ \mathbf{IN} \ \text{numbers and} \ \mathbf{OUT}\\ &&& \text{numbers. Some OUT numbers are missing. The rule says add 5.}\\ & \mathbf{My \ Job:} && \text{Fill in the other OUT numbers.}\\ & \mathbf{Plan:} && \text{Add} \ 5 \ \text{to each} \ \mathbf{IN} \ \text{number to get the} \ \mathbf{OUT} \ \text{number.}\\ & \mathbf{Solve:}\end{align*}

In Out
1 6
4 9
5 10
3 8
2 7

\begin{align*}& \mathbf{Check:} && \text{Start with the IN number. Count up:} \ 1, 2, 3, 4, 5, 6\\ &&& \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ 4, 5, 6, 7, 8, 9\\ &&& \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ 5, 6, 7, 8, 9, 10\\ &&& \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ 3, 4, 5, 6, 7, 8\\ &&& \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ 2, 3, 4, 5, 6, 7\end{align*}

#### Earlier Problem Revisited

We can use the problem solving steps to help us solve this problem.

\begin{align*}& \mathbf{Describe:} && \text{The box is an} \ \mathbf{Add \ 2} \ \text{machine. The table has} \ \mathbf{IN} \ \text{numbers and} \ \mathbf{OUT}\\ &&& \text{numbers. Some OUT numbers are missing.}\\ & \mathbf{My \ Job:} && \text{Fill in the other OUT numbers.}\\ & \mathbf{Plan:} && \text{Add} \ 2 \ \text{to each} \ \mathbf{IN} \ \text{number to get the} \ \mathbf{OUT} \ \text{number.}\\ & \mathbf{Solve:}\end{align*}

In Out
1 3
4 6
3 5
0 2
5 7

\begin{align*}& \mathbf{Check:} && \text{Start with the IN number. Count up:} \ 4, 5, 6\\ &&& \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ 3, 4, 5\\ &&& \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ 0, 1, 2\\ &&& \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \ \ 5, 6, 7\end{align*}

### Vocabulary

A function is an example of a rule that states a relationship between two quantities. In this concept, our rule told us how to go from the in number to the out number in each

### Examples

Follow the rules. Complete the tables.

In Out
6 10
0 4
3 7
4 8
5 9

In Out
7 9
5 7
8 10
3 5
6 8

In Out
5 9
2 1
6 10
8 12
3 7

In Out
0 6
6 12
2 8
3 9
4 10

### Review

Follow the rules. Complete the tables.

 3 7

### Notes/Highlights Having trouble? Report an issue.

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Date Created:
Jan 18, 2013
Mar 23, 2016

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