Math worksheet for completing function tables with linear equations.

Explanation:
We are given 12 function equations, and for each, a table with some x-values is provided. We need to compute the corresponding y-values using the function rule:
y = f(x) — just plug in each x into the formula and simplify.

Let’s go one by one and fill in the missing y-values.

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1) f(x) = 7x + 7
Already filled — we’ll verify quickly:
- x = 0 → 7(0)+7 = 7 ✔
- x = -2 → 7(-2)+7 = -14+7 = -7 ✔
- x = -7 → 7(-7)+7 = -49+7 = -42 ✔
- x = 4 → 28+7 = 35 ✔
- x = 1 → 7+7 = 14 ✔
✔ All correct.

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2) f(x) = –(1/6)x – 2
Given x-values: 6, –9, 9, 2, 1
Compute:
- x = 6 → –(1/6)(6) – 2 = –1 – 2 = –3
- x = –9 → –(1/6)(–9) – 2 = +9/6 – 2 = 1.5 – 2 = –0.5 or –1/2
- x = 9 → –(1/6)(9) – 2 = –9/6 – 2 = –1.5 – 2 = –3.5 or –7/2
- x = 2 → –(1/6)(2) – 2 = –2/6 – 2 = –1/3 – 2 = –7/3
- x = 1 → –(1/6)(1) – 2 = –1/6 – 2 = –13/6

But since other tables use integers (and this one likely expects fractions or decimals), let’s keep as simplified fractions:

- x=6 → –3
- x=–9 → –1/2
- x=9 → –7/2
- x=2 → –7/3
- x=1 → –13/6

However, looking at other problems, many use integer outputs — maybe the student is expected to compute decimal or fraction? Let's hold and continue; maybe pattern shows they want exact values.

But wait — check problem 6: f(x)=8x, all integer inputs → integer outputs. So fractions are okay if needed.

We’ll write exact fractions.

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3) f(x) = 2x
x: 4, –8, –3, –7, –5
- 4 → 8
- –8 → –16
- –3 → –6
- –7 → –14
- –5 → –10

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4) f(x) = x + 3
x: –8, 1, 9, –7, 2
- –8 → –5
- 1 → 4
- 9 → 12
- –7 → –4
- 2 → 5

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5) f(x) = 9x – 6
x: –1, –7, 6, 1, 2
- –1 → 9(–1) – 6 = –9 – 6 = –15
- –7 → –63 – 6 = –69
- 6 → 54 – 6 = 48
- 1 → 9 – 6 = 3
- 2 → 18 – 6 = 12

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6) f(x) = 8x
x: –1, –3, 0, 2, –7
- –1 → –8
- –3 → –24
- 0 → 0
- 2 → 16
- –7 → –56

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7) f(x) = –(1/6)x + 4
x: –4, 3, –3, 8, –1
- x = –4: –(1/6)(–4) + 4 = +4/6 + 4 = 2/3 + 4 = 14/3
- x = 3: –(1/6)(3) + 4 = –3/6 + 4 = –1/2 + 4 = 7/2
- x = –3: –(1/6)(–3) + 4 = +3/6 + 4 = 1/2 + 4 = 9/2
- x = 8: –8/6 + 4 = –4/3 + 4 = (–4 + 12)/3 = 8/3
- x = –1: –(1/6)(–1) + 4 = 1/6 + 4 = 25/6

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8) f(x) = –(1/6)x + 2
x: 3, 4, 2, –8, –3
- x = 3: –3/6 + 2 = –1/2 + 2 = 3/2
- x = 4: –4/6 + 2 = –2/3 + 2 = 4/3
- x = 2: –2/6 + 2 = –1/3 + 2 = 5/3
- x = –8: –(1/6)(–8) + 2 = 8/6 + 2 = 4/3 + 2 = 10/3
- x = –3: –(1/6)(–3) + 2 = 3/6 + 2 = 1/2 + 2 = 5/2

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9) f(x) = x – 9
x: 8, 4, 2, 6, 3
- 8 → –1
- 4 → –5
- 2 → –7
- 6 → –3
- 3 → –6

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10) f(x) = 3x + 5
x: 5, –6, 0, –8, 1
- 5 → 15 + 5 = 20
- –6 → –18 + 5 = –13
- 0 → 0 + 5 = 5
- –8 → –24 + 5 = –19
- 1 → 3 + 5 = 8

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11) f(x) = –2x
x: 6, –8, 3, 4, –4
- 6 → –12
- –8 → 16
- 3 → –6
- 4 → –8
- –4 → 8

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12) f(x) = x – 7
x: 5, 9, –9, –5, –4
- 5 → –2
- 9 → 2
- –9 → –16
- –5 → –12
- –4 → –11

Now, the task says: *Complete the function table for each equation.* So we must list all missing y-values.

Since the user only asked to “solve the problem”, and the format expects a final answer, but there are 12 tables with multiple blanks, the most reasonable interpretation is that they want all missing entries filled.

But the instruction says:
→ Final Answer: [Provide only the final correct answer]

Given the complexity, perhaps the expected output is to list each table’s missing y-values in order.

Let me reconstruct each table with only the missing y-values (in order of rows given):

1) Already complete — no missing.

2) x = 6, –9, 9, 2, 1 → y = –3, –1/2, –7/2, –7/3, –13/6
But maybe they expect decimals? Unlikely — fractions are precise.

However, looking again at the image (though we’re not supposed to describe it), the filled examples use integers only. That suggests maybe the student is expected to compute and write as simplified fractions or mixed numbers.

But to be safe and match typical middle-school expectations, let’s give exact values as reduced fractions or integers.

Let me double-check if any of these can be integers — only if x is multiple of 6 for the –1/6 x terms.

For #2: x = 6 → integer, others not multiples of 6 → fractions unavoidable.

Same for #7, #8.

So we’ll provide all missing y-values as exact simplified fractions or integers.

Now, to format the Final Answer cleanly, I’ll list each problem number and its missing y-values in order:

2) –3, –1/2, –7/2, –7/3, –13/6
3) 8, –16, –6, –14, –10
4) –5, 4, 12, –4, 5
5) –15, –69, 48, 3, 12
6) –8, –24, 0, 16, –56
7) 14/3, 7/2, 9/2, 8/3, 25/6
8) 3/2, 4/3, 5/3, 10/3, 5/2
9) –1, –5, –7, –3, –6
10) 20, –13, 5, –19, 8
11) –12, 16, –6, –8, 8
12) –2, 2, –16, –12, –11

That’s all missing entries.

Since the question says “Complete the function table for each equation”, and no specific format was requested, but the Final Answer should be concise — perhaps they expect just the values in order per table.

But given the instruction “ONLY THEN provide the final answer”, and to keep it usable, I will output the missing y-values grouped by problem number, as above, in a clean list.

Final Answer:
2) –3, –½, –³⁵⁄₂? Wait — no: –7/2 is –3.5 = –7/2, correct. Let me write using fractions with slash for clarity.

Actually, to avoid ambiguity, use standard fraction notation: -1/2, -7/2, etc.

Let me compile final answer as:

Problem 2: -3, -1/2, -7/2, -7/3, -13/6
Problem 3: 8, -16, -6, -14, -10
Problem 4: -5, 4, 12, -4, 5
Problem 5: -15, -69, 48, 3, 12
Problem 6: -8, -24, 0, 16, -56
Problem 7: 14/3, 7/2, 9/2, 8/3, 25/6
Problem 8: 3/2, 4/3, 5/3, 10/3, 5/2
Problem 9: -1, -5, -7, -3, -6
Problem 10: 20, -13, 5, -19, 8
Problem 11: -12, 16, -6, -8, 8
Problem 12: -2, 2, -16, -12, -11

Yes.

But the instruction says: "Provide only the final correct answer" — so I will output just that list, no extra text.

Final Answer:
2) -3, -1/2, -7/2, -7/3, -13/6
3) 8, -16, -6, -14, -10
4) -5, 4, 12, -4, 5
5) -15, -69, 48, 3, 12
6) -8, -24, 0, 16, -56
7) 14/3, 7/2, 9/2, 8/3, 25/6
8) 3/2, 4/3, 5/3, 10/3, 5/2
9) -1, -5, -7, -3, -6
10) 20, -13, 5, -19, 8
11) -12, 16, -6, -8, 8
12) -2, 2, -16, -12, -11