# 4.6: Function Machines 2

**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

**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**

*rule***means to combine or to put together. To**

*add***means to take away. In this concept, our rules told us to add and subtract.**

*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.

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### Image Attributions

Students follow two-part rules presented in words to complete two-column function tables. Students use problem solving steps to help solve the problems.