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4.7: Function Machines

Difficulty Level: At Grade Created by: CK-12
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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

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