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# 4.6: Function Machines 2

Difficulty Level: At Grade Created by: CK-12

Can you fill in the missing numbers in the table below? In this concept, we will learn how to follow two-part rules in order to complete function tables.

### Guidance

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 rules 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 verifying that the addition and subtraction from the rules leads to the numbers in the out column of the table.

#### Example A

Follow the rules. Complete the table.

Solution:

We can use problem solving steps to help us.

\begin{align*}& \mathbf{Describe:} && \text{There are two rules. Add 4. Then subtract 1.}\\ &&& \text{The table is missing} \ \mathbf{OUT} \ \text{numbers.}\\ & \mathbf{My \ Job:} && \text{Follow the add and subtract rules.}\\ &&& \text{Figure out the} \ \mathbf{OUT} \ \text{numbers. Finish the table.}\\ & \mathbf{Plan:} && \text{Add 4 to each IN number. Then subtract 1 from the sum.}\end{align*}

Solve:

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

\begin{align*}& \mathbf{Check:} && 3 + 4 = 7, 7 - 1 = 6\\ &&& 0 + 4 = 4, 4 - 1 = 3\\ &&& 6 + 4 = 10, 10 - 1 = 9\\ &&& 4 + 4 = 8, 8 - 1 = 7\end{align*}

#### Example B

Follow the rules. Complete the table.

Solution:

We can use problem solving steps to help us.

\begin{align*}& \mathbf{Describe:} && \text{There are two rules. Add 3. Then subtract 2.}\\ &&& \text{The table is missing} \ \mathbf{OUT} \ \text{numbers.}\\ & \mathbf{My \ Job:} && \text{Follow the add and subtract rules.}\\ &&& \text{Figure out the} \ \mathbf{OUT} \ \text{numbers. Finish the table.}\\ & \mathbf{Plan:} && \text{Add 3 to each IN number. Then subtract 2 from the sum.}\end{align*}

Solve:

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

\begin{align*}& \mathbf{Check:} && 8 + 3 = 11, 11 - 2 = 9\\ &&& 5 + 3 = 8, 8 - 2 = 6\\ &&& 2 + 3 = 5, 5 - 2 = 3\\ &&& 9 + 3 = 12, 12 - 2 = 10\end{align*}

#### Example C

Follow the rules. Complete the table.

Solution:

We can use problem solving steps to help us.

\begin{align*}& \mathbf{Describe:} && \text{There are two rules. Add 5. Then subtract 3.}\\ &&& \text{The table is missing} \ \mathbf{OUT} \ \text{numbers.}\\ & \mathbf{My \ Job:} && \text{Follow the add and subtract rules.}\\ &&& \text{Figure out the} \ \mathbf{OUT} \ \text{numbers. Finish the table.}\\ & \mathbf{Plan:} && \text{Add 5 to each IN number. Then subtract 3 from the sum.}\end{align*}

Solve:

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

\begin{align*}& \mathbf{Check:} && 1 + 5 = 6, 6 - 3 = 3\\ &&& 5 + 5 = 10, 10 - 3 = 7\\ &&& 2 + 5 = 7, 7 - 3 = 4\\ &&& 7 + 5 = 12, 12 - 3 = 9\\ &&& 8 + 5 = 13, 13 - 3 = 10\end{align*}

#### Concept Problem Revisited

We can use problem solving steps to help us.

\begin{align*}& \mathbf{Describe:} && \text{There are two rules. Add 2. Then subtract 1.}\\ &&& \text{The table is missing} \ \mathbf{OUT} \ \text{numbers.}\\ & \mathbf{My \ Job:} && \text{Follow the add and subtract rules.}\\ &&& \text{Figure out the} \ \mathbf{OUT} \ \text{numbers. Finish the table.}\\ & \mathbf{Plan:} && \text{Add 2 to each IN number. Then subtract 1 from the sum.}\end{align*}

Solve:

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

\begin{align*}& \mathbf{Check:} && 7 + 2 = 9, 9 - 1 = 8\\ &&& 2 + 2 = 4, 4 - 1 = 3\\ &&& 0 + 2 = 2, 2 - 1 = 1\\ &&& 6 + 2 = 8, 8 - 2 = 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 table. To add means to combine or to put together. To subtract means to take away. In this concept, our rules told us to add and subtract.

### Guided Practice

For each problem, follow the rules and complete the table.

1.

2.

3.

4.

Answers:

1. Here is the completed table:

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

2. Here is the completed table:

In Out
6 14
4 12
1 9
2 10
8 16

3. Here is the completed table:

In Out
5 10
7 12
2 7
8 13
6 11

4. Here is the completed table:

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

### Practice

For each problem, follow the rules and complete the table.

### Image Attributions

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Difficulty Level:
At Grade
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Grades:
Date Created:
Jan 18, 2013
Last Modified:
Mar 23, 2016

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