Function Table Worksheets | Function Table & In and Out Boxes ... - Free Printable

Let's solve each function table step by step. We are given a function $ f(x) $ and a set of $ x $-values. For each, we will compute $ y = f(x) $ by substituting the value of $ x $ into the equation.

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1) $ f(x) = 7x + 7 $

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

✔ Already filled correctly.

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2) $ f(x) = \frac{1}{6}x - 2 $

| x | y |
|---|---|
| 6 | $ \frac{1}{6}(6) - 2 = 1 - 2 = -1 $ |
| -9 | $ \frac{1}{6}(-9) - 2 = -1.5 - 2 = -3.5 $ |
| 9 | $ \frac{1}{6}(9) - 2 = 1.5 - 2 = -0.5 $ |
| 2 | $ \frac{1}{6}(2) - 2 = \frac{1}{3} - 2 = -\frac{5}{3} \approx -1.67 $ |
| 1 | $ \frac{1}{6}(1) - 2 = \frac{1}{6} - 2 = -\frac{11}{6} \approx -1.83 $ |

So:

| x | y |
|---|---|
| 6 | -1 |
| -9 | -3.5 |
| 9 | -0.5 |
| 2 | -5/3 or -1.67 |
| 1 | -11/6 or -1.83 |

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3) $ f(x) = 2x $

| x | y |
|---|---|
| 4 | $ 2(4) = 8 $ |
| -8 | $ 2(-8) = -16 $ |
| -3 | $ 2(-3) = -6 $ |
| -7 | $ 2(-7) = -14 $ |
| -5 | $ 2(-5) = -10 $ |

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

---

4) $ f(x) = x + 3 $

| x | y |
|---|---|
| -8 | $ -8 + 3 = -5 $ |
| 1 | $ 1 + 3 = 4 $ |
| 9 | $ 9 + 3 = 12 $ |
| -7 | $ -7 + 3 = -4 $ |
| 2 | $ 2 + 3 = 5 $ |

| x | y |
|---|---|
| -8 | -5 |
| 1 | 4 |
| 9 | 12 |
| -7 | -4 |
| 2 | 5 |

---

5) $ f(x) = 9x - 6 $

| x | y |
|---|---|
| -1 | $ 9(-1) - 6 = -9 - 6 = -15 $ |
| -7 | $ 9(-7) - 6 = -63 - 6 = -69 $ |
| 6 | $ 9(6) - 6 = 54 - 6 = 48 $ |
| 1 | $ 9(1) - 6 = 9 - 6 = 3 $ |
| 2 | $ 9(2) - 6 = 18 - 6 = 12 $ |

| x | y |
|---|---|
| -1 | -15 |
| -7 | -69 |
| 6 | 48 |
| 1 | 3 |
| 2 | 12 |

---

6) $ f(x) = 8x $

| x | y |
|---|---|
| -1 | $ 8(-1) = -8 $ |
| -3 | $ 8(-3) = -24 $ |
| 0 | $ 8(0) = 0 $ |
| 2 | $ 8(2) = 16 $ |
| -7 | $ 8(-7) = -56 $ |

| x | y |
|---|---|
| -1 | -8 |
| -3 | -24 |
| 0 | 0 |
| 2 | 16 |
| -7 | -56 |

---

7) $ f(x) = -\frac{1}{9}x + 4 $

| x | y |
|---|---|
| -4 | $ -\frac{1}{9}(-4) + 4 = \frac{4}{9} + 4 = \frac{4}{9} + \frac{36}{9} = \frac{40}{9} \approx 4.44 $ |
| 3 | $ -\frac{1}{9}(3) + 4 = -\frac{1}{3} + 4 = \frac{11}{3} \approx 3.67 $ |
| -3 | $ -\frac{1}{9}(-3) + 4 = \frac{1}{3} + 4 = \frac{13}{3} \approx 4.33 $ |
| 8 | $ -\frac{1}{9}(8) + 4 = -\frac{8}{9} + 4 = \frac{28}{9} \approx 3.11 $ |
| -1 | $ -\frac{1}{9}(-1) + 4 = \frac{1}{9} + 4 = \frac{37}{9} \approx 4.11 $ |

| x | y |
|---|---|
| -4 | 40/9 ≈ 4.44 |
| 3 | 11/3 ≈ 3.67 |
| -3 | 13/3 ≈ 4.33 |
| 8 | 28/9 ≈ 3.11 |
| -1 | 37/9 ≈ 4.11 |

---

8) $ f(x) = \frac{1}{6}x + 2 $

| x | y |
|---|---|
| 3 | $ \frac{1}{6}(3) + 2 = 0.5 + 2 = 2.5 $ |
| 4 | $ \frac{1}{6}(4) + 2 = \frac{2}{3} + 2 = \frac{8}{3} \approx 2.67 $ |
| 2 | $ \frac{1}{6}(2) + 2 = \frac{1}{3} + 2 = \frac{7}{3} \approx 2.33 $ |
| -8 | $ \frac{1}{6}(-8) + 2 = -\frac{4}{3} + 2 = \frac{2}{3} \approx 0.67 $ |
| -3 | $ \frac{1}{6}(-3) + 2 = -0.5 + 2 = 1.5 $ |

| x | y |
|---|---|
| 3 | 2.5 |
| 4 | 8/3 ≈ 2.67 |
| 2 | 7/3 ≈ 2.33 |
| -8 | 2/3 ≈ 0.67 |
| -3 | 1.5 |

---

9) $ f(x) = x - 9 $

| x | y |
|---|---|
| 8 | $ 8 - 9 = -1 $ |
| 4 | $ 4 - 9 = -5 $ |
| 2 | $ 2 - 9 = -7 $ |
| 6 | $ 6 - 9 = -3 $ |
| 3 | $ 3 - 9 = -6 $ |

| x | y |
|---|---|
| 8 | -1 |
| 4 | -5 |
| 2 | -7 |
| 6 | -3 |
| 3 | -6 |

---

10) $ f(x) = 3x + 5 $

| x | y |
|---|---|
| 5 | $ 3(5) + 5 = 15 + 5 = 20 $ |
| -6 | $ 3(-6) + 5 = -18 + 5 = -13 $ |
| 0 | $ 3(0) + 5 = 0 + 5 = 5 $ |
| -8 | $ 3(-8) + 5 = -24 + 5 = -19 $ |
| 1 | $ 3(1) + 5 = 3 + 5 = 8 $ |

| x | y |
|---|---|
| 5 | 20 |
| -6 | -13 |
| 0 | 5 |
| -8 | -19 |
| 1 | 8 |

---

11) $ f(x) = -2x $

| x | y |
|---|---|
| 6 | $ -2(6) = -12 $ |
| -8 | $ -2(-8) = 16 $ |
| 3 | $ -2(3) = -6 $ |
| 4 | $ -2(4) = -8 $ |
| -4 | $ -2(-4) = 8 $ |

| x | y |
|---|---|
| 6 | -12 |
| -8 | 16 |
| 3 | -6 |
| 4 | -8 |
| -4 | 8 |

---

12) $ f(x) = x - 7 $

| x | y |
|---|---|
| 5 | $ 5 - 7 = -2 $ |
| 9 | $ 9 - 7 = 2 $ |
| -9 | $ -9 - 7 = -16 $ |
| -5 | $ -5 - 7 = -12 $ |
| -4 | $ -4 - 7 = -11 $ |

| x | y |
|---|---|
| 5 | -2 |
| 9 | 2 |
| -9 | -16 |
| -5 | -12 |
| -4 | -11 |

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✔ Final Answer Summary (All Tables Completed):

#### 1) $ f(x) = 7x + 7 $
| x | y |
|---|---|
| 0 | 7 |
| -2 | -7 |
| -7 | -42 |
| 4 | 35 |
| 1 | 14 |

#### 2) $ f(x) = \frac{1}{6}x - 2 $
| x | y |
|---|---|
| 6 | -1 |
| -9 | -3.5 |
| 9 | -0.5 |
| 2 | -5/3 ≈ -1.67 |
| 1 | -11/6 ≈ -1.83 |

#### 3) $ f(x) = 2x $
| x | y |
|---|---|
| 4 | 8 |
| -8 | -16 |
| -3 | -6 |
| -7 | -14 |
| -5 | -10 |

#### 4) $ f(x) = x + 3 $
| x | y |
|---|---|
| -8 | -5 |
| 1 | 4 |
| 9 | 12 |
| -7 | -4 |
| 2 | 5 |

#### 5) $ f(x) = 9x - 6 $
| x | y |
|---|---|
| -1 | -15 |
| -7 | -69 |
| 6 | 48 |
| 1 | 3 |
| 2 | 12 |

#### 6) $ f(x) = 8x $
| x | y |
|---|---|
| -1 | -8 |
| -3 | -24 |
| 0 | 0 |
| 2 | 16 |
| -7 | -56 |

#### 7) $ f(x) = -\frac{1}{9}x + 4 $
| x | y |
|---|---|
| -4 | 40/9 ≈ 4.44 |
| 3 | 11/3 ≈ 3.67 |
| -3 | 13/3 ≈ 4.33 |
| 8 | 28/9 ≈ 3.11 |
| -1 | 37/9 ≈ 4.11 |

#### 8) $ f(x) = \frac{1}{6}x + 2 $
| x | y |
|---|---|
| 3 | 2.5 |
| 4 | 8/3 ≈ 2.67 |
| 2 | 7/3 ≈ 2.33 |
| -8 | 2/3 ≈ 0.67 |
| -3 | 1.5 |

#### 9) $ f(x) = x - 9 $
| x | y |
|---|---|
| 8 | -1 |
| 4 | -5 |
| 2 | -7 |
| 6 | -3 |
| 3 | -6 |

#### 10) $ f(x) = 3x + 5 $
| x | y |
|---|---|
| 5 | 20 |
| -6 | -13 |
| 0 | 5 |
| -8 | -19 |
| 1 | 8 |

#### 11) $ f(x) = -2x $
| x | y |
|---|---|
| 6 | -12 |
| -8 | 16 |
| 3 | -6 |
| 4 | -8 |
| -4 | 8 |

#### 12) $ f(x) = x - 7 $
| x | y |
|---|---|
| 5 | -2 |
| 9 | 2 |
| -9 | -16 |
| -5 | -12 |
| -4 | -11 |

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✔ Explanation:

To complete a function table:
1. Take each given $ x $-value.
2. Plug it into the function $ f(x) $.
3. Simplify to find $ y = f(x) $.
4. Fill in the corresponding $ y $-value.

This process works for linear functions like these. The key is careful substitution and arithmetic, especially with fractions and negatives.

Let me know if you'd like this as a printable PDF or formatted worksheet!