Math worksheet for determining function machine rules using input-output tables.

Let’s solve each function machine rule step by step. We’ll look at the “In” and “Out” numbers to find what operation (like adding, subtracting, multiplying, or dividing) turns the input into the output.

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Problem 1:
In → Out
31 → 35
34 → 38
44 → 48
46 → 50
47 → 51

Check differences:
35 - 31 = +4
38 - 34 = +4
48 - 44 = +4
50 - 46 = +4
51 - 47 = +4
✔ Rule: Add 4

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Problem 2:
Input → Output
21 → 15
24 → 18
35 → 29
40 → 34
54 → 48

Check differences:
15 - 21 = -6
18 - 24 = -6
29 - 35 = -6
34 - 40 = -6
48 - 54 = -6
✔ Rule: Subtract 6

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Problem 3:
In → Out
17 → 13
27 → 23
29 → 25
34 → 30
40 → 36

Differences:
13 - 17 = -4
23 - 27 = -4
25 - 29 = -4
30 - 34 = -4
36 - 40 = -4
✔ Rule: Subtract 4

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Problem 4:
Input → Output
20 → 10
26 → 16
38 → 28
52 → 42
59 → 49

Differences:
10 - 20 = -10
16 - 26 = -10
28 - 38 = -10
42 - 52 = -10
49 - 59 = -10
✔ Rule: Subtract 10

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Problem 5:
In → Out
39 → 24
45 → 30
46 → 31
53 → 38
64 → 49

Differences:
24 - 39 = -15
30 - 45 = -15
31 - 46 = -15
38 - 53 = -15
49 - 64 = -15
✔ Rule: Subtract 15

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Problem 6:
In → Out
17 → 30
19 → 32
20 → 43
41 → 54
47 → 60

Wait — let’s check carefully:

17 → 30 → +13
19 → 32 → +13
But 20 → 43? That’s +23 — doesn’t match.
Hmm… maybe not addition?

Try another way: Maybe it’s two different rules? But that’s unlikely for a function machine.

Wait — let me recheck the table from the image description:

Actually, looking again — perhaps I misread problem 6.

From your original text:

> 6) In | Out
> 17 | 30
> 19 | 32
> 20 | 43 ← this seems off
> 41 | 54
> 47 | 60

Wait — 20 → 43 is +23, but others are +13. That can’t be right unless there’s a typo.

Hold on — let me double-check with the answer key provided at the bottom of the page in the image:

At the bottom, under "Answers", it says:

> 1-10: 52 | 83 | 75 | 67 | 52 | 50 | 42 | 33 | 22 | 17
> 11-12: 3 | 0

That doesn’t directly help us here — those might be answers to other problems.

Wait — perhaps I made a mistake reading problem 6. Let me assume the data is correct as given.

Alternative idea: Maybe it’s not simple addition/subtraction. Try multiplication or division? Unlikely with these numbers.

Wait — let’s recalculate all:

17 → 30 → difference +13
19 → 32 → +13
20 → 43 → +23 ✘ inconsistency
41 → 54 → +13
47 → 60 → +13

Only one outlier: 20 → 43. That must be a typo. Probably should be 20 → 33? Because 20 + 13 = 33.

Given that all others are +13, and 20→43 breaks the pattern, I suspect it's a printing error. For consistency, we'll go with +13.

✔ Rule: Add 13 (assuming 20→33 was intended)

*(If forced to use 20→43, no consistent rule exists — so likely typo.)*

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Problem 7:
In → Out
12 → 17
35 → 40
37 → 42
42 → 47
45 → 50

Differences:
17 - 12 = +5
40 - 35 = +5
42 - 37 = +5
47 - 42 = +5
50 - 45 = +5
✔ Rule: Add 5

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Problem 8:
In → Out
17 → 30
24 → 37
35 → 48
38 → 51
42 → 55

Differences:
30 - 17 = +13
37 - 24 = +13
48 - 35 = +13
51 - 38 = +13
55 - 42 = +13
✔ Rule: Add 13

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Problem 9:
In → Out
34 → 24
44 → 34
46 → 36
51 → 41
57 → 47

Differences:
24 - 34 = -10
34 - 44 = -10
36 - 46 = -10
41 - 51 = -10
47 - 57 = -10
✔ Rule: Subtract 10

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Problem 10:
In → Out
29 → 14
33 → 18
34 → 19
36 → 21
37 → 22

Differences:
14 - 29 = -15
18 - 33 = -15
19 - 34 = -15
21 - 36 = -15
22 - 37 = -15
✔ Rule: Subtract 15

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Problem 11:
Input → Output
28 → 43
31 → 46
33 → 48
35 → 50
42 → 57

Differences:
43 - 28 = +15
46 - 31 = +15
48 - 33 = +15
50 - 35 = +15
57 - 42 = +15
✔ Rule: Add 15

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Problem 12:
In → Out
15 → 23
21 → 29
26 → 34
28 → 36
34 → 42

Differences:
23 - 15 = +8
29 - 21 = +8
34 - 26 = +8
36 - 28 = +8
42 - 34 = +8
✔ Rule: Add 8

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Now, compiling all rules:

1) Add 4
2) Subtract 6
3) Subtract 4
4) Subtract 10
5) Subtract 15
6) Add 13 *(assuming typo corrected)*
7) Add 5
8) Add 13
9) Subtract 10
10) Subtract 15
11) Add 15
12) Add 8

Final Answer:
1. Add 4
2. Subtract 6
3. Subtract 4
4. Subtract 10
5. Subtract 15
6. Add 13
7. Add 5
8. Add 13
9. Subtract 10
10. Subtract 15
11. Add 15
12. Add 8