# 4.7: Function Machines

**At Grade**Created by: CK-12

**Function Machines – Complete two-step function tables**

For these problems, students follow rules presented in words and with symbols to complete two-column function tables. Each of the rules requires two computational steps. Problems 1-12 use addition followed by subtraction. Problems 13 -20 mix the sequence of addition then subtraction and subtraction then addition.

**Solutions**

1.

In |
Out |
---|---|

5 | 8 |

3 | 6 |

0 | 3 |

6 | 9 |

4 | 7 |

2.

In |
Out |
---|---|

4 | 5 |

8 | 9 |

5 | 6 |

2 | 3 |

9 | 10 |

3.

In |
Out |
---|---|

1 | 3 |

5 | 7 |

2 | 4 |

7 | 9 |

8 | 10 |

4.

In |
Out |
---|---|

4 | 8 |

6 | 10 |

3 | 7 |

1 | 3 |

5 | 9 |

5.

In |
Out |
---|---|

6 | 14 |

4 | 12 |

1 | 9 |

2 | 10 |

8 | 16 |

6.

In |
Out |
---|---|

5 | 10 |

7 | 12 |

2 | 7 |

8 | 13 |

6 | 11 |

7.

In |
Out |
---|---|

2 | 3 |

8 | 9 |

5 | 6 |

4 | 5 |

8 |

8.

In |
Out |
---|---|

2 | 9 |

0 | 7 |

3 | 10 |

5 | 12 |

1 | 8 |

9.

In |
Out |
---|---|

4 | 13 |

7 | 16 |

2 | 11 |

9 | 18 |

5 | 14 |

10.

In |
Out |
---|---|

8 | 16 |

3 | 11 |

9 | 17 |

5 | 13 |

7 | 15 |

11.

In |
Out |
---|---|

2 | 8 |

5 | 11 |

7 | 13 |

1 | 7 |

8 | 14 |

12.

In |
Out |
---|---|

8 | 15 |

2 | 9 |

6 | 13 |

4 | 11 |

1 | 8 |

13.

In |
Out |
---|---|

4 | 3 |

8 | 7 |

5 | 4 |

2 | 1 |

7 | 6 |

14.

In |
Out |
---|---|

4 | 2 |

2 | 0 |

8 | 6 |

6 | 4 |

3 | 1 |

15.

In |
Out |
---|---|

9 | 16 |

12 | 19 |

5 | 12 |

10 | 17 |

8 | 15 |

16.

In |
Out |
---|---|

7 | 15 |

3 | 11 |

9 | 17 |

2 | 10 |

5 | 13 |

17.

In |
Out |
---|---|

1 | 6 |

7 | 12 |

4 | 9 |

9 | 14 |

2 | 7 |

18.

In |
Out |
---|---|

2 | 6 |

5 | 9 |

9 | 13 |

3 | 7 |

0 | 4 |

19.

In |
Out |
---|---|

16 | 12 |

10 | 6 |

9 | 5 |

11 | 7 |

14 | 10 |

20.

In |
Out |
---|---|

4 | 11 |

7 | 14 |

11 | 18 |

5 | 12 |

9 | 16 |

\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 an IN number. Then subtract 1 from the sum.}\end{align*}

**Solve:**

In |
Out |
---|---|

4 | 5 |

7 | 6 |

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*}

Follow the rules.

Complete the tables.

**Extra for Experts: Function Machines – Complete two-step function tables**

**Solutions**

1.

In |
Out |
---|---|

6 | 12 |

2 | 8 |

8 | 14 |

1 | 7 |

9 | 15 |

2.

In |
Out |
---|---|

7 | 13 |

4 | 10 |

5 | 11 |

9 | 15 |

3 | 9 |

3.

In |
Out |
---|---|

2 | 5 |

5 | 8 |

0 | 3 |

6 | 9 |

4 | 7 |

4.

In |
Out |
---|---|

7 | 10 |

3 | 6 |

9 | 12 |

4 | 7 |

1 | 4 |

5.

In |
Out |
---|---|

6 | 5 |

8 | 7 |

3 | 2 |

9 | 8 |

4 | 3 |

6.

In |
Out |
---|---|

3 | 0 |

8 | 5 |

6 | 3 |

5 | 2 |

7 | 4 |

7.

In |
Out |
---|---|

2 | 3 |

5 | 6 |

0 | 1 |

6 | 7 |

4 | 5 |

8.

In |
Out |
---|---|

7 | 10 |

3 | 6 |

9 | 12 |

4 | 7 |

1 | 4 |

9.

In |
Out |
---|---|

6 | 10 |

2 | 6 |

10 | 14 |

8 | 12 |

5 | 9 |

10.

In |
Out |
---|---|

0 | 3 |

3 | 6 |

7 | 10 |

9 | 12 |

4 | 7 |

11.

In |
Out |
---|---|

1 | 5 |

9 | 13 |

6 | 10 |

8 | 12 |

7 | 11 |

12.

In |
Out |
---|---|

10 | 7 |

8 | 5 |

12 | 9 |

6 | 3 |

9 | 6 |