Complete the function table for each equation.

Let’s solve each function table step by step. For each equation, we plug in the given x-values to find the corresponding y-values (which is f(x)).

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1) f(x) = 7x + 7

- x = 0 → y = 7(0) + 7 = 7
- x = -2 → y = 7(-2) + 7 = -14 + 7 = -7
- x = -7 → y = 7(-7) + 7 = -49 + 7 = -42
- x = 4 → y = 7(4) + 7 = 28 + 7 = 35
- x = 1 → y = 7(1) + 7 = 7 + 7 = 14

✔ Already filled correctly.

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2) f(x) = -¹/₈x - 2

We’ll compute each:

- x = 6 → y = -(1/8)(6) - 2 = -6/8 - 2 = -3/4 - 2 = -2.75 or -11/4
But since other answers are integers, let’s check if maybe it's meant to be decimal? Wait — actually, let’s keep as fractions unless told otherwise. But looking at context, probably expects decimals or simplified fractions.

Wait — let me recalculate carefully:

Actually, for school level, they might expect decimal or fraction. Let’s do exact values.

But note: -¹/₈ * 6 = -6/8 = -3/4 → then -3/4 - 2 = -3/4 - 8/4 = -11/4 → which is -2.75

But perhaps better to write as mixed number? Or decimal? Since others are integers, maybe this one allows fractions.

Wait — let’s look again. The problem says “complete the table” — and in #1, all were integers. Maybe I made a mistake?

Wait — no, the function is f(x) = -¹/₈x - 2. So with x=6, it’s not integer. That’s okay.

But let’s proceed with exact values.

Actually, let’s use decimals for simplicity unless specified.

So:

- x = 6 → y = -0.125*6 - 2 = -0.75 - 2 = -2.75
- x = -9 → y = -0.125*(-9) - 2 = 1.125 - 2 = -0.875
- x = 9 → y = -0.125*9 - 2 = -1.125 - 2 = -3.125
- x = 2 → y = -0.125*2 - 2 = -0.25 - 2 = -2.25
- x = 1 → y = -0.125*1 - 2 = -0.125 - 2 = -2.125

Hmm, these are messy. Maybe the problem expects fractions?

Let’s try fractions:

f(x) = -¹/₈x - 2 = (-x/8) - 2

- x=6 → -6/8 - 2 = -3/4 - 8/4 = -11/4
- x=-9 → -(-9)/8 - 2 = 9/8 - 16/8 = -7/8
- x=9 → -9/8 - 16/8 = -25/8
- x=2 → -2/8 - 16/8 = -1/4 - 2 = -9/4? Wait: -2/8 = -1/4; -1/4 - 2 = -1/4 - 8/4 = -9/4
- x=1 → -1/8 - 16/8 = -17/8

This is getting complicated. Perhaps there’s a typo? Or maybe I should just go with decimals rounded? But the original image shows some green numbers — like in #1, they have 7, -7, -42, 35, 14 — all integers.

Wait — looking back at the user’s image description — in problem 2, the function is written as f(x) = -¹/₈x - 2. But maybe it’s -1/(8x)? No, that would be unusual. Probably it’s (-1/8)*x - 2.

Given that, I think we must accept non-integers. But let’s see what the expected format is. In the answer key shown in the image (green text), only #1 has answers filled. Others are blank. So we need to fill them.

Perhaps for consistency, we'll use decimals to two places? Or fractions? Let’s use fractions for accuracy.

But to match typical middle/high school worksheets, they often use decimals when fractions are involved.

Alternatively, maybe the coefficient is -1/8, so let’s calculate exactly.

I think best to use fractions unless decimal is cleaner.

But let’s move on and come back. Actually, let’s do all problems first, then verify.

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3) f(x) = 2x

Simple multiplication:

- x=4 → y=8
- x=-8 → y=-16
- x=-3 → y=-6
- x=-7 → y=-14
- x=-5 → y=-10

All integers.

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4) f(x) = x + 3

Add 3 to each x:

- x=-8 → y=-5
- x=1 → y=4
- x=9 → y=12
- x=-7 → y=-4
- x=2 → y=5

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5) f(x) = 9x - 6

Multiply by 9, subtract 6:

- x=-1 → 9*(-1)-6 = -9-6 = -15
- x=-7 → 9*(-7)-6 = -63-6 = -69
- x=6 → 9*6-6 = 54-6 = 48
- x=1 → 9*1-6 = 9-6 = 3
- x=2 → 9*2-6 = 18-6 = 12

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6) f(x) = 8x

Just multiply by 8:

- x=-1 → -8
- x=-3 → -24
- x=0 → 0
- x=2 → 16
- x=-7 → -56

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7) f(x) = -¹/₉x + 4

Again, fractional coefficient.

f(x) = (-1/9)x + 4

Compute each:

- x=-4 → (-1/9)*(-4) + 4 = 4/9 + 4 = 4/9 + 36/9 = 40/9 ≈ 4.444...
- x=3 → (-1/9)*3 + 4 = -3/9 + 4 = -1/3 + 4 = 11/3 ≈ 3.666...
- x=-3 → (-1/9)*(-3) + 4 = 3/9 + 4 = 1/3 + 4 = 13/3 ≈ 4.333...
- x=8 → (-1/9)*8 + 4 = -8/9 + 36/9 = 28/9 ≈ 3.111...
- x=-1 → (-1/9)*(-1) + 4 = 1/9 + 36/9 = 37/9 ≈ 4.111...

Messy again. Perhaps the worksheet expects decimals? Or maybe I misread the function.

Looking back: in the user’s message, it’s written as "f(x) = - \frac{1}{9}x + 4" — so yes, -1/9 times x plus 4.

In many such worksheets, they might avoid fractions in input, but here inputs are integers, outputs may not be.

To be consistent, I’ll use fractions unless decimal is terminating and simple.

But for now, let’s continue.

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8) f(x) = ¹/₅x + 2

f(x) = (1/5)x + 2

- x=3 → 3/5 + 2 = 3/5 + 10/5 = 13/5 = 2.6
- x=4 → 4/5 + 2 = 4/5 + 10/5 = 14/5 = 2.8
- x=2 → 2/5 + 2 = 2/5 + 10/5 = 12/5 = 2.4
- x=-8 → -8/5 + 2 = -8/5 + 10/5 = 2/5 = 0.4
- x=-3 → -3/5 + 2 = -3/5 + 10/5 = 7/5 = 1.4

Still fractions.

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9) f(x) = x - 9

Subtract 9 from each x:

- x=8 → -1
- x=4 → -5
- x=2 → -7
- x=6 → -3
- x=3 → -6

All integers.

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10) f(x) = 3x + 5

Multiply by 3, add 5:

- x=5 → 15+5=20
- x=-6 → -18+5=-13
- x=0 → 0+5=5
- x=-8 → -24+5=-19
- x=1 → 3+5=8

Integers.

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11) f(x) = -2x

Multiply by -2:

- x=6 → -12
- x=-8 → 16
- x=3 → -6
- x=4 → -8
- x=-4 → 8

Integers.

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12) f(x) = x - 7

Subtract 7:

- x=5 → -2
- x=9 → 2
- x=-9 → -16
- x=-5 → -12
- x=-4 → -11

Integers.

---

Now, going back to problems with fractions: #2 and #7 and #8.

For #2: f(x) = -¹/₈x - 2

Let me write answers as decimals for practicality, since fractions are repeating or complex.

- x=6 → -0.75 - 2 = -2.75
- x=-9 → -(-9)/8 - 2 = 9/8 - 2 = 1.125 - 2 = -0.875
- x=9 → -9/8 - 2 = -1.125 - 2 = -3.125
- x=2 → -2/8 - 2 = -0.25 - 2 = -2.25
- x=1 → -1/8 - 2 = -0.125 - 2 = -2.125

Similarly for #7: f(x) = -¹/₉x + 4

- x=-4 → (4/9) + 4 = 4.444... → 4.44 if rounded, but better to leave as fraction? Or perhaps the worksheet expects exact fractions.

Since this is for a student, and to avoid confusion, I’ll provide both fractional and decimal forms where necessary, but in the final answer, I’ll use the most appropriate form based on context.

Looking at the initial problem #1, all answers are integers, and in the green text, they are integers. For problems with fractions, likely the expected answer is in decimal or simplified fraction.

But to be precise, let's use fractions for exactness.

However, upon second thought, in many standardized worksheets, if the function has a fraction, they design x-values to give integer outputs. Here, for #2, x=6 gives -11/4, which is not integer. Similarly for others.

Perhaps there's a mistake in my interpretation. Let me double-check the function for #2.

In the user's message: "2) f(x) = - \frac{1}{8}x - 2"

Yes.

Maybe it's -1/(8x)? But that would be undefined at x=0, and not linear. Unlikely.

Another possibility: perhaps the coefficient is -1/8, and they want decimal answers.

I think for the sake of completing the task, I'll use decimal representations rounded to three decimal places if needed, but since some are exact, I'll use exact decimals.

For example:

#2:
- x=6: -2.75
- x=-9: -0.875
- x=9: -3.125
- x=2: -2.25
- x=1: -2.125

These are exact decimals.

Similarly for #7:
- x=-4: 4 + 4/9 = 4.444... → but 4/9 is repeating, so perhaps leave as fraction 40/9? But that's not nice.

Wait, 40/9 is approximately 4.444, but in math class, sometimes they prefer fractions.

To resolve this, I recall that in the original image, for problem 1, they have integer answers, and for others, they are blank, so we need to fill them as per calculation.

Perhaps the teacher expects students to calculate and write the exact value, whether fraction or decimal.

But to make it clean, I'll use fractions for #2, #7, #8.

Let me define:

For #2: f(x) = - (1/8)x - 2 = (-x - 16)/8 ? Not helpful.

Better to compute numerically.

I think for the final answer, I'll list the y-values as calculated, using fractions where decimals are repeating, but for #2, the decimals terminate, so use decimals.

For #7 and #8, decimals repeat, so use fractions.

Let's do that.

Final decision:

- For functions with integer coefficients, output integers.
- For #2: use decimals (since they terminate)
- For #7 and #8: use fractions (since decimals repeat)

But #8: f(x) = (1/5)x + 2, and x=3,4,2,-8,-3 — all give tenths, which are terminating decimals: 2.6, 2.8, etc. So can use decimals.

Similarly, #7: -1/9x +4, x=-4: 4/9 +4 = 40/9 = 4.444... repeating, so better as fraction.

This is inconsistent.

Perhaps the worksheet intends for all answers to be in simplest form, and for fractions, leave as improper fractions.

To simplify, I'll provide the answers as follows:

For each problem, calculate y = f(x) and write the numerical value.

After careful consideration, I will use the following approach for the final answer:

- If the result is an integer, write the integer.
- If it's a terminating decimal, write the decimal.
- If it's a repeating decimal, write the fraction.

But for consistency in presentation, since this is a table, and to match the style of #1, I'll use decimals for all non-integers, rounding to three decimal places if necessary, but for exact values, use exact decimals.

For #7, 40/9 = 4.444..., which is repeating, so perhaps write as 4.\overline{4}, but that's not standard for tables.

Given the complexity, and since this is likely for middle school, I suspect that the functions with fractions are meant to be calculated as is, and students can use calculators or leave as fractions.

But to provide a clean answer, I'll calculate all and present in the table format with the values.

Let me compile all answers.

First, let's list all problems with their y-values.

Problem 1: f(x) = 7x + 7
Already given: y = [7, -7, -42, 35, 14] for x=[0,-2,-7,4,1]

Problem 2: f(x) = - (1/8)x - 2
x | y
6 | - (6/8) - 2 = -0.75 - 2 = -2.75
-9 | - (-9/8) - 2 = 9/8 - 2 = 1.125 - 2 = -0.875
9 | -9/8 - 2 = -1.125 - 2 = -3.125
2 | -2/8 - 2 = -0.25 - 2 = -2.25
1 | -1/8 - 2 = -0.125 - 2 = -2.125

So y = [-2.75, -0.875, -3.125, -2.25, -2.125]

Problem 3: f(x) = 2x
y = [8, -16, -6, -14, -10]

Problem 4: f(x) = x + 3
y = [-5, 4, 12, -4, 5]

Problem 5: f(x) = 9x - 6
y = [-15, -69, 48, 3, 12]

Problem 6: f(x) = 8x
y = [-8, -24, 0, 16, -56]

Problem 7: f(x) = - (1/9)x + 4
x | y
-4 | - (1/9)*(-4) + 4 = 4/9 + 4 = 40/9 ≈ 4.444... but let's keep as 40/9
3 | -3/9 + 4 = -1/3 + 4 = 11/3
-3 | - (-3)/9 + 4 = 3/9 + 4 = 1/3 + 4 = 13/3
8 | -8/9 + 4 = -8/9 + 36/9 = 28/9
-1 | - (-1)/9 + 4 = 1/9 + 4 = 37/9

So y = [40/9, 11/3, 13/3, 28/9, 37/9]

Problem 8: f(x) = (1/5)x + 2
x | y
3 | 3/5 + 2 = 0.6 + 2 = 2.6
4 | 4/5 + 2 = 0.8 + 2 = 2.8
2 | 2/5 + 2 = 0.4 + 2 = 2.4
-8 | -8/5 + 2 = -1.6 + 2 = 0.4
-3 | -3/5 + 2 = -0.6 + 2 = 1.4

So y = [2.6, 2.8, 2.4, 0.4, 1.4]

Problem 9: f(x) = x - 9
y = [8-9= -1, 4-9= -5, 2-9= -7, 6-9= -3, 3-9= -6]

Problem 10: f(x) = 3x + 5
y = [3*5+5=20, 3*(-6)+5= -18+5= -13, 3*0+5=5, 3*(-8)+5= -24+5= -19, 3*1+5=8]

Problem 11: f(x) = -2x
y = [-2*6= -12, -2*(-8)=16, -2*3= -6, -2*4= -8, -2*(-4)=8]

Problem 12: f(x) = x - 7
y = [5-7= -2, 9-7=2, -9-7= -16, -5-7= -12, -4-7= -11]

Now, for the final answer, I need to present the completed tables.

Since the user asked to solve the problem, and the problem is to complete the function tables, I will list the y-values for each problem in order.

To make it clear, I'll group by problem number.

Also, for problems with fractions, I'll use the fractional form for accuracy, as decimals may not be exact.

But for #2, the decimals are exact, so I'll use decimals.

For #7, fractions are better.

For #8, decimals are fine.

So let's finalize:

Problem 2 y-values: -2.75, -0.875, -3.125, -2.25, -2.125

Problem 7 y-values: 40/9, 11/3, 13/3, 28/9, 37/9

Problem 8 y-values: 2.6, 2.8, 2.4, 0.4, 1.4

Others are integers.

Now, for the Final Answer, I'll write the y-values for each problem in sequence.

Since the table has specific x-orders, I'll list y in the order of x given.

Let me write the final answer as a list of y-values for each problem.

Final Answer:

1) y = 7, -7, -42, 35, 14
2) y = -2.75, -0.875, -3.125, -2.25, -2.125
3) y = 8, -16, -6, -14, -10
4) y = -5, 4, 12, -4, 5
5) y = -15, -69, 48, 3, 12
6) y = -8, -24, 0, 16, -56
7) y = 40/9, 11/3, 13/3, 28/9, 37/9
8) y = 2.6, 2.8, 2.4, 0.4, 1.4
9) y = -1, -5, -7, -3, -6
10) y = 20, -13, 5, -19, 8
11) y = -12, 16, -6, -8, 8
12) y = -2, 2, -16, -12, -11

I think this is accurate.

For problem 7, to make it neater, I could write as mixed numbers, but improper fractions are fine.

40/9 = 4 4/9, but in math, improper is acceptable.

Similarly, 11/3 = 3 2/3, etc.

But for consistency, I'll leave as improper fractions.

Now, for the boxed answer, since it's multiple parts, I'll present it as above.

The instruction is to put the final answer in \boxed{}, but for multiple values, perhaps box each problem's y-list.

Since it's a table completion, the final answer is the set of y-values for each problem.

I think for clarity, I'll write:

Final Answer:

For each problem, the y-values in order are:

1) \boxed{7}, \boxed{-7}, \boxed{-42}, \boxed{35}, \boxed{14}
2) \boxed{-2.75}, \boxed{-0.875}, \boxed{-3.125}, \boxed{-2.25}, \boxed{-2.125}
3) \boxed{8}, \boxed{-16}, \boxed{-6}, \boxed{-14}, \boxed{-10}
4) \boxed{-5}, \boxed{4}, \boxed{12}, \boxed{-4}, \boxed{5}
5) \boxed{-15}, \boxed{-69}, \boxed{48}, \boxed{3}, \boxed{12}
6) \boxed{-8}, \boxed{-24}, \boxed{0}, \boxed{16}, \boxed{-56}
7) \boxed{\dfrac{40}{9}}, \boxed{\dfrac{11}{3}}, \boxed{\dfrac{13}{3}}, \boxed{\dfrac{28}{9}}, \boxed{\dfrac{37}{9}}
8) \boxed{2.6}, \boxed{2.8}, \boxed{2.4}, \boxed{0.4}, \boxed{1.4}
9) \boxed{-1}, \boxed{-5}, \boxed{-7}, \boxed{-3}, \boxed{-6}
10) \boxed{20}, \boxed{-13}, \boxed{5}, \boxed{-19}, \boxed{8}
11) \boxed{-12}, \boxed{16}, \boxed{-6}, \boxed{-8}, \boxed{8}
12) \boxed{-2}, \boxed{2}, \boxed{-16}, \boxed{-12}, \boxed{-11}

This should be correct.

Note: For problem 2, the values are exact decimals, so no issue.

For problem 7, fractions are exact.

For problem 8, decimals are exact since denominators are 5.

So this is accurate.