Define, evaluate, and compare functions | 8th Grade Math | Math Chimp - Free Printable

Let's solve each function table step by step. We'll plug in the given values of $ x $ into each equation to find the corresponding $ y $ values.

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1) $ y = -\frac{1}{3}x - 9 $

We substitute each $ x $ value:

- $ x = 9 $:
$ y = -\frac{1}{3}(9) - 9 = -3 - 9 = -12 $

- $ x = -1 $:
$ y = -\frac{1}{3}(-1) - 9 = \frac{1}{3} - 9 = -8\frac{2}{3} $ or $ -\frac{25}{3} $

- $ x = 5 $:
$ y = -\frac{1}{3}(5) - 9 = -\frac{5}{3} - 9 = -\frac{5}{3} - \frac{27}{3} = -\frac{32}{3} \approx -10.67 $

- $ x = -7 $:
$ y = -\frac{1}{3}(-7) - 9 = \frac{7}{3} - 9 = \frac{7}{3} - \frac{27}{3} = -\frac{20}{3} \approx -6.67 $

- $ x = 3 $:
$ y = -\frac{1}{3}(3) - 9 = -1 - 9 = -10 $

✔ Completed Table:
| x | y |
|----|-----------|
| 9 | -12 |
| -1 | -8⅔ |
| 5 | -10⅔ |
| -7 | -6⅔ |
| 3 | -10 |

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2) $ y = 5x $

- $ x = -5 $: $ y = 5(-5) = -25 $
- $ x = -4 $: $ y = 5(-4) = -20 $
- $ x = -1 $: $ y = 5(-1) = -5 $
- $ x = 0 $: $ y = 5(0) = 0 $
- $ x = 2 $: $ y = 5(2) = 10 $

✔ Completed Table:
| x | y |
|----|-----|
| -5 | -25 |
| -4 | -20 |
| -1 | -5 |
| 0 | 0 |
| 2 | 10 |

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5) $ y = -\frac{1}{8}x + 6 $

- $ x = 5 $: $ y = -\frac{1}{8}(5) + 6 = -\frac{5}{8} + 6 = 5\frac{3}{8} $
- $ x = -2 $: $ y = -\frac{1}{8}(-2) + 6 = \frac{2}{8} + 6 = \frac{1}{4} + 6 = 6.25 $
- $ x = 7 $: $ y = -\frac{1}{8}(7) + 6 = -\frac{7}{8} + 6 = 5\frac{1}{8} $
- $ x = 6 $: $ y = -\frac{1}{8}(6) + 6 = -\frac{6}{8} + 6 = -\frac{3}{4} + 6 = 5.25 $
- $ x = -9 $: $ y = -\frac{1}{8}(-9) + 6 = \frac{9}{8} + 6 = 1\frac{1}{8} + 6 = 7.125 $

✔ Completed Table:
| x | y |
|----|----------|
| 5 | 5⅜ |
| -2 | 6.25 |
| 7 | 5⅛ |
| 6 | 5.25 |
| -9 | 7.125 |

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6) $ y = x - 6 $

- $ x = 7 $: $ y = 7 - 6 = 1 $
- $ x = 2 $: $ y = 2 - 6 = -4 $
- $ x = 0 $: $ y = 0 - 6 = -6 $
- $ x = 10 $: $ y = 10 - 6 = 4 $
- $ x = -3 $: $ y = -3 - 6 = -9 $

Wait — looking at the table, only three values are shown: 7, 2, 0. Let’s assume it’s just those three.

But wait — the image shows only three rows for #6: 7, 2, 0

So:
- $ x = 7 $: $ y = 1 $
- $ x = 2 $: $ y = -4 $
- $ x = 0 $: $ y = -6 $

✔ Completed Table:
| x | y |
|----|-----|
| 7 | 1 |
| 2 | -4 |
| 0 | -6 |

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9) $ y = 7x - 5 $

- $ x = 9 $: $ y = 7(9) - 5 = 63 - 5 = 58 $
- $ x = 7 $: $ y = 7(7) - 5 = 49 - 5 = 44 $
- $ x = 3 $: $ y = 7(3) - 5 = 21 - 5 = 16 $
- $ x = -9 $: $ y = 7(-9) - 5 = -63 - 5 = -68 $
- $ x = 2 $: $ y = 7(2) - 5 = 14 - 5 = 9 $

✔ Completed Table:
| x | y |
|----|-----|
| 9 | 58 |
| 7 | 44 |
| 3 | 16 |
| -9 | -68 |
| 2 | 9 |

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10) $ y = -4x $

- $ x = 7 $: $ y = -4(7) = -28 $
- $ x = 6 $: $ y = -4(6) = -24 $
- $ x = 2 $: $ y = -4(2) = -8 $
- $ x = 0 $: $ y = -4(0) = 0 $
- $ x = -3 $: $ y = -4(-3) = 12 $

Wait — the table shows only 7, 6, 2 → so let’s use only those:

- $ x = 7 $: $ y = -28 $
- $ x = 6 $: $ y = -24 $
- $ x = 2 $: $ y = -8 $

✔ Completed Table:
| x | y |
|----|-----|
| 7 | -28 |
| 6 | -24 |
| 2 | -8 |

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✔ Final Answer Summary:

#### 1) $ y = -\frac{1}{3}x - 9 $
| x | y |
|----|-----------|
| 9 | -12 |
| -1 | -8⅔ |
| 5 | -10⅔ |
| -7 | -6⅔ |
| 3 | -10 |

#### 2) $ y = 5x $
| x | y |
|----|-----|
| -5 | -25 |
| -4 | -20 |
| -1 | -5 |
| 0 | 0 |
| 2 | 10 |

#### 5) $ y = -\frac{1}{8}x + 6 $
| x | y |
|----|----------|
| 5 | 5⅜ |
| -2 | 6.25 |
| 7 | 5⅛ |
| 6 | 5.25 |
| -9 | 7.125 |

#### 6) $ y = x - 6 $
| x | y |
|----|-----|
| 7 | 1 |
| 2 | -4 |
| 0 | -6 |

#### 9) $ y = 7x - 5 $
| x | y |
|----|-----|
| 9 | 58 |
| 7 | 44 |
| 3 | 16 |
| -9 | -68 |
| 2 | 9 |

#### 10) $ y = -4x $
| x | y |
|----|-----|
| 7 | -28 |
| 6 | -24 |
| 2 | -8 |

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🔍 Explanation:

For each problem, we used substitution: take each $ x $ value and plug it into the given equation to compute $ y $. This is how you complete a function table.

> 💡 Tip: Always follow the order of operations (PEMDAS) when simplifying expressions.

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