Function Table Worksheet for Algebra Practice

The task involves completing function tables for various linear functions. Each table provides a set of input values (\( x \)) and requires you to calculate the corresponding output values (\( f(x) \)) using the given function rule. Below, I will solve each problem step by step.

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Problem 1: \( f(x) = x - 7 \)

#### Function Rule:
\[ f(x) = x - 7 \]

#### Input Values:
\[ x = -7, -2, -1, 0, 3, 5 \]

#### Calculations:
- For \( x = -7 \):
\[
f(-7) = -7 - 7 = -14
\]
- For \( x = -2 \):
\[
f(-2) = -2 - 7 = -9
\]
- For \( x = -1 \):
\[
f(-1) = -1 - 7 = -8
\]
- For \( x = 0 \):
\[
f(0) = 0 - 7 = -7
\]
- For \( x = 3 \):
\[
f(3) = 3 - 7 = -4
\]
- For \( x = 5 \):
\[
f(5) = 5 - 7 = -2
\]

#### Output Values:
\[
f(x) = -14, -9, -8, -7, -4, -2
\]

---

Problem 2: \( f(x) = x + 8 \)

#### Function Rule:
\[ f(x) = x + 8 \]

#### Input Values:
\[ x = -7, -2, -1, 0, 3, 5 \]

#### Calculations:
- For \( x = -7 \):
\[
f(-7) = -7 + 8 = 1
\]
- For \( x = -2 \):
\[
f(-2) = -2 + 8 = 6
\]
- For \( x = -1 \):
\[
f(-1) = -1 + 8 = 7
\]
- For \( x = 0 \):
\[
f(0) = 0 + 8 = 8
\]
- For \( x = 3 \):
\[
f(3) = 3 + 8 = 11
\]
- For \( x = 5 \):
\[
f(5) = 5 + 8 = 13
\]

#### Output Values:
\[
f(x) = 1, 6, 7, 8, 11, 13
\]

---

Problem 3: \( f(x) = x - 6 \)

#### Function Rule:
\[ f(x) = x - 6 \]

#### Input Values:
\[ x = 0, 3, 5, 8, 11, 14 \]

#### Calculations:
- For \( x = 0 \):
\[
f(0) = 0 - 6 = -6
\]
- For \( x = 3 \):
\[
f(3) = 3 - 6 = -3
\]
- For \( x = 5 \):
\[
f(5) = 5 - 6 = -1
\]
- For \( x = 8 \):
\[
f(8) = 8 - 6 = 2
\]
- For \( x = 11 \):
\[
f(11) = 11 - 6 = 5
\]
- For \( x = 14 \):
\[
f(14) = 14 - 6 = 8
\]

#### Output Values:
\[
f(x) = -6, -3, -1, 2, 5, 8
\]

---

Problem 4: \( f(x) = 8 - x \)

#### Function Rule:
\[ f(x) = 8 - x \]

#### Input Values:
\[ x = -7, -2, -1, 0, 3, 5 \]

#### Calculations:
- For \( x = -7 \):
\[
f(-7) = 8 - (-7) = 8 + 7 = 15
\]
- For \( x = -2 \):
\[
f(-2) = 8 - (-2) = 8 + 2 = 10
\]
- For \( x = -1 \):
\[
f(-1) = 8 - (-1) = 8 + 1 = 9
\]
- For \( x = 0 \):
\[
f(0) = 8 - 0 = 8
\]
- For \( x = 3 \):
\[
f(3) = 8 - 3 = 5
\]
- For \( x = 5 \):
\[
f(5) = 8 - 5 = 3
\]

#### Output Values:
\[
f(x) = 15, 10, 9, 8, 5, 3
\]

---

Problem 5: \( f(x) = -x + 3 \)

#### Function Rule:
\[ f(x) = -x + 3 \]

#### Input Values:
\[ x = -7, -2, -1, 0, 3, 5 \]

#### Calculations:
- For \( x = -7 \):
\[
f(-7) = -(-7) + 3 = 7 + 3 = 10
\]
- For \( x = -2 \):
\[
f(-2) = -(-2) + 3 = 2 + 3 = 5
\]
- For \( x = -1 \):
\[
f(-1) = -(-1) + 3 = 1 + 3 = 4
\]
- For \( x = 0 \):
\[
f(0) = -(0) + 3 = 0 + 3 = 3
\]
- For \( x = 3 \):
\[
f(3) = -(3) + 3 = -3 + 3 = 0
\]
- For \( x = 5 \):
\[
f(5) = -(5) + 3 = -5 + 3 = -2
\]

#### Output Values:
\[
f(x) = 10, 5, 4, 3, 0, -2
\]

---

Problem 6: \( f(x) = -x - 3 \)

#### Function Rule:
\[ f(x) = -x - 3 \]

#### Input Values:
\[ x = -7, -2, -1, 0, 3, 5 \]

#### Calculations:
- For \( x = -7 \):
\[
f(-7) = -(-7) - 3 = 7 - 3 = 4
\]
- For \( x = -2 \):
\[
f(-2) = -(-2) - 3 = 2 - 3 = -1
\]
- For \( x = -1 \):
\[
f(-1) = -(-1) - 3 = 1 - 3 = -2
\]
- For \( x = 0 \):
\[
f(0) = -(0) - 3 = 0 - 3 = -3
\]
- For \( x = 3 \):
\[
f(3) = -(3) - 3 = -3 - 3 = -6
\]
- For \( x = 5 \):
\[
f(5) = -(5) - 3 = -5 - 3 = -8
\]

#### Output Values:
\[
f(x) = 4, -1, -2, -3, -6, -8
\]

---

Problem 7: \( f(x) = -2x \)

#### Function Rule:
\[ f(x) = -2x \]

#### Input Values:
\[ x = -7, -2, -1, 0, 3, 5 \]

#### Calculations:
- For \( x = -7 \):
\[
f(-7) = -2(-7) = 14
\]
- For \( x = -2 \):
\[
f(-2) = -2(-2) = 4
\]
- For \( x = -1 \):
\[
f(-1) = -2(-1) = 2
\]
- For \( x = 0 \):
\[
f(0) = -2(0) = 0
\]
- For \( x = 3 \):
\[
f(3) = -2(3) = -6
\]
- For \( x = 5 \):
\[
f(5) = -2(5) = -10
\]

#### Output Values:
\[
f(x) = 14, 4, 2, 0, -6, -10
\]

---

Problem 8: \( f(x) = 2x \)

#### Function Rule:
\[ f(x) = 2x \]

#### Input Values:
\[ x = -7, -2, -1, 0, 3, 5 \]

#### Calculations:
- For \( x = -7 \):
\[
f(-7) = 2(-7) = -14
\]
- For \( x = -2 \):
\[
f(-2) = 2(-2) = -4
\]
- For \( x = -1 \):
\[
f(-1) = 2(-1) = -2
\]
- For \( x = 0 \):
\[
f(0) = 2(0) = 0
\]
- For \( x = 3 \):
\[
f(3) = 2(3) = 6
\]
- For \( x = 5 \):
\[
f(5) = 2(5) = 10
\]

#### Output Values:
\[
f(x) = -14, -4, -2, 0, 6, 10
\]

---

Final Answers:

1. \( f(x) = x - 7 \): \(\boxed{-14, -9, -8, -7, -4, -2}\)
2. \( f(x) = x + 8 \): \(\boxed{1, 6, 7, 8, 11, 13}\)
3. \( f(x) = x - 6 \): \(\boxed{-6, -3, -1, 2, 5, 8}\)
4. \( f(x) = 8 - x \): \(\boxed{15, 10, 9, 8, 5, 3}\)
5. \( f(x) = -x + 3 \): \(\boxed{10, 5, 4, 3, 0, -2}\)
6. \( f(x) = -x - 3 \): \(\boxed{4, -1, -2, -3, -6, -8}\)
7. \( f(x) = -2x \): \(\boxed{14, 4, 2, 0, -6, -10}\)
8. \( f(x) = 2x \): \(\boxed{-14, -4, -2, 0, 6, 10}\)

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Final Answer Boxed:
\[
\boxed{
\begin{aligned}
1. & \quad -14, -9, -8, -7, -4, -2 \\
2. & \quad 1, 6, 7, 8, 11, 13 \\
3. & \quad -6, -3, -1, 2, 5, 8 \\
4. & \quad 15, 10, 9, 8, 5, 3 \\
5. & \quad 10, 5, 4, 3, 0, -2 \\
6. & \quad 4, -1, -2, -3, -6, -8 \\
7. & \quad 14, 4, 2, 0, -6, -10 \\
8. & \quad -14, -4, -2, 0, 6, 10 \\
\end{aligned}
}
\]