Function Machine-Determining Rule - Determine the Input-to-Output Rule

Sep 30, 2026

Uploaded by Elsa

Function machine determining rule worksheet tasks learners to infer an unknown transformation from given input and output number sequences. For each problem, a set of “in” values maps to a list of “out” values, and students must choose which arithmetic rule using Q best matches. Answer options include addition, subtraction, multiplication, and division by specific constants. An answer key provides the correct choices for each item.

LanguageEnglish

CategoryExam

FormatPDF

Pages3

Reading Time8 min

AccessFree to download

Determine the Function Machine Rule

Problems 1-3

Problems 4-6

Problems 7-9

Answers

Function Machine-Determining Rule Name: | Determine which number sentence best matches the function machine.
1)

in
out 50 41 51 42 42 33 44 35 59 50
2)

in
out 30 22 52 44 25 17 29 21 43 35
3)

in
out 25 34 42 51 50 59 36 45 17 26
If each input is 'Q' which rule could the function machine be using?
A. Q + 9
B. Q-9
C. Q × 9
D. Q ÷ 9
If each input is 'Q' which rule could the function machine be using?
A. Q + 8
B. Q-8
C. Q × 8
D. Q ÷ 8
If each input is 'Q' which rule could the function machine be using?
A. Q + 9
B. Q-9
C. Q × 9
D. Q ÷ 9
4)

in
out 54 40 36 22 50 36 37 23 25 11
5)

in
out 31 38 35 42 12 19 28 35 50 57
6)

in
out 49 54 12 17 16 21 30 35 25 30
If each input is 'Q' which rule could the function machine be using?
A. Q + 14
B. Q-14
C. Q × 14
D. Q ÷ 14
If each input is 'Q' which rule could the function machine be using?
A. Q + 7
B. Q-7
C. Q × 7
D. Q ÷ 7
If each input is 'Q' which rule could the function machine be using?
A. Q + 5
B. Q-5
C. Q × 5
D. Q ÷ 5
7)

in
out 25 11 28 14 34 20 45 31 58 44
8)

in
out 32 44 43 55 48 60 47 59 26 38
9)

in
out 25 12 60 47 26 13 57 44 61 48
If each input is 'Q' which rule could the function machine be using?
A. Q + 14
B. Q-14
C. Q × 14
D. Q ÷ 14
If each input is 'Q' which rule could the function machine be using?
A. Q + 12
B. Q-12
C. Q × 12
D. Q ÷ 12
If each input is 'Q' which rule could the function machine be using?
A. Q + 13
B. Q-13
C. Q × 13
D. Q ÷ 13 | | | | | | Answers | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | | | | | | | 1.
2.
3.
4.
5.
6.
7.
8.
9. | | | | | 1-9 | 89 | 78 | 67 | 56 | 44 | 33 | 22 | 11 | 0 | [Math](Math www.CommonCoreSheets.com 6)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 6)[ 6](Math www.CommonCoreSheets.com 6) Function Machine-Determining Rule Name: Answer Key | Determine which number sentence best matches the function machine.
1)

in
out 50 41 51 42 42 33 44 35 59 50
2)

in
out 30 22 52 44 25 17 29 21 43 35
3)

in
out 25 34 42 51 50 59 36 45 17 26
If each input is 'Q' which rule could the function machine be using?
A. Q + 9
B. Q-9
C. Q × 9
D. Q ÷ 9
If each input is 'Q' which rule could the function machine be using?
A. Q + 8
B. Q-8
C. Q × 8
D. Q ÷ 8
If each input is 'Q' which rule could the function machine be using?
A. Q + 9
B. Q-9
C. Q × 9
D. Q ÷ 9
4)

in
out 54 40 36 22 50 36 37 23 25 11
5)

in
out 31 38 35 42 12 19 28 35 50 57
6)

in
out 49 54 12 17 16 21 30 35 25 30
If each input is 'Q' which rule could the function machine be using?
A. Q + 14
B. Q-14
C. Q × 14
D. Q ÷ 14
If each input is 'Q' which rule could the function machine be using?
A. Q + 7
B. Q-7
C. Q × 7
D. Q ÷ 7
If each input is 'Q' which rule could the function machine be using?
A. Q + 5
B. Q-5
C. Q × 5
D. Q ÷ 5
7)

in
out 25 11 28 14 34 20 45 31 58 44
8)

in
out 32 44 43 55 48 60 47 59 26 38
9)

in
out 25 12 60 47 26 13 57 44 61 48
If each input is 'Q' which rule could the function machine be using?
A. Q + 14
B. Q-14
C. Q × 14
D. Q ÷ 14
If each input is 'Q' which rule could the function machine be using?
A. Q + 12
B. Q-12
C. Q × 12
D. Q ÷ 12
If each input is 'Q' which rule could the function machine be using?
A. Q + 13
B. Q-13
C. Q × 13
D. Q ÷ 13 | | | | | | Answers | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | | | | | | | 1. B
2. B
3. A
4. B
5. A
6. A
7. B
8. A
9. B | | | | | 1-9 | 89 | 78 | 67 | 56 |

FAQs

How do you determine the rule for a function machine from “in” and “out” values?

Compare the pattern between the given “in” numbers and their corresponding “out” numbers. Then test which of the provided operations (+, -, ×, ÷) with the listed constant produces the observed outputs.

What answer choices are available for each question?

Each question provides four options describing a possible rule for Q: Q + constant, Q - constant, Q × constant, or Q ÷ constant.

What is the purpose of the answer key in the worksheet?

The answer key lists the correct letter choice for each numbered problem, allowing students to verify their selected rules.

Sep 30, 2026

Uploaded by Elsa