Function table practice worksheet with various mathematical rules and input-output problems.

Let's solve each part of the function tables step by step.

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Part 1: Complete the function tables using given rules

#### 1. Subtract 4
Rule: $ Y = X - 4 $

| X | Y |
|---|---|
| 4 | ? |
| ? | 12 |
| 10 | ? |

- For $ X = 4 $: $ Y = 4 - 4 = 0 $
- For $ Y = 12 $: $ X - 4 = 12 \Rightarrow X = 16 $
- For $ X = 10 $: $ Y = 10 - 4 = 6 $

✔ Completed Table:
| X | Y |
|---|---|
| 4 | 0 |
| 16 | 12 |
| 10 | 6 |

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#### 2. Add 7; divide by 2
Rule: $ Y = \frac{X + 7}{2} $

| X | Y |
|---|---|
| ? | 4 |
| 3 | ? |
| 5 | ? |

- For $ Y = 4 $:
$ \frac{X + 7}{2} = 4 \Rightarrow X + 7 = 8 \Rightarrow X = 1 $
- For $ X = 3 $:
$ Y = \frac{3 + 7}{2} = \frac{10}{2} = 5 $
- For $ X = 5 $:
$ Y = \frac{5 + 7}{2} = \frac{12}{2} = 6 $

✔ Completed Table:
| X | Y |
|---|---|
| 1 | 4 |
| 3 | 5 |
| 5 | 6 |

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#### 3. Multiply by 3; add 1
Rule: $ Y = 3X + 1 $

| X | Y |
|---|---|
| ? | 1 |
| ? | 13 |
| 12 | ? |

- For $ Y = 1 $:
$ 3X + 1 = 1 \Rightarrow 3X = 0 \Rightarrow X = 0 $
- For $ Y = 13 $:
$ 3X + 1 = 13 \Rightarrow 3X = 12 \Rightarrow X = 4 $
- For $ X = 12 $:
$ Y = 3(12) + 1 = 36 + 1 = 37 $

✔ Completed Table:
| X | Y |
|---|---|
| 0 | 1 |
| 4 | 13 |
| 12 | 37 |

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Part 2: Complete function tables using equations

#### 1. Rule: $ y = x - 5 $

| Input (x) | Output (y) |
|----------|------------|
| 10 | ? |
| 12 | ? |
| 14 | ? |

- $ x = 10 $: $ y = 10 - 5 = 5 $
- $ x = 12 $: $ y = 12 - 5 = 7 $
- $ x = 14 $: $ y = 14 - 5 = 9 $

✔
| Input (x) | Output (y) |
|----------|------------|
| 10 | 5 |
| 12 | 7 |
| 14 | 9 |

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#### 2. Rule: $ y = x + 2 $

| Input (x) | Output (y) |
|----------|------------|
| 3 | ? |
| 4 | ? |
| 5 | ? |

- $ x = 3 $: $ y = 3 + 2 = 5 $
- $ x = 4 $: $ y = 4 + 2 = 6 $
- $ x = 5 $: $ y = 5 + 2 = 7 $

✔
| Input (x) | Output (y) |
|----------|------------|
| 3 | 5 |
| 4 | 6 |
| 5 | 7 |

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#### 3. Rule: $ y = 4x - 3 $

| Input (x) | Output (y) |
|----------|------------|
| 1 | ? |
| 2 | ? |
| 3 | ? |

- $ x = 1 $: $ y = 4(1) - 3 = 4 - 3 = 1 $
- $ x = 2 $: $ y = 4(2) - 3 = 8 - 3 = 5 $
- $ x = 3 $: $ y = 4(3) - 3 = 12 - 3 = 9 $

✔
| Input (x) | Output (y) |
|----------|------------|
| 1 | 1 |
| 2 | 5 |
| 3 | 9 |

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#### 4. Rule: $ y = 6x - 10 $

| Input (x) | Output (y) |
|----------|------------|
| 6 | ? |
| 7 | ? |
| 8 | ? |

- $ x = 6 $: $ y = 6(6) - 10 = 36 - 10 = 26 $
- $ x = 7 $: $ y = 6(7) - 10 = 42 - 10 = 32 $
- $ x = 8 $: $ y = 6(8) - 10 = 48 - 10 = 38 $

✔
| Input (x) | Output (y) |
|----------|------------|
| 6 | 26 |
| 7 | 32 |
| 8 | 38 |

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#### 5. Rule: $ y = 7x + 9 $

| Input (x) | Output (y) |
|----------|------------|
| 2 | ? |
| 3 | ? |
| 4 | ? |

- $ x = 2 $: $ y = 7(2) + 9 = 14 + 9 = 23 $
- $ x = 3 $: $ y = 7(3) + 9 = 21 + 9 = 30 $
- $ x = 4 $: $ y = 7(4) + 9 = 28 + 9 = 37 $

✔
| Input (x) | Output (y) |
|----------|------------|
| 2 | 23 |
| 3 | 30 |
| 4 | 37 |

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#### 6. Rule: $ y = 8x + 2 $

| Input (x) | Output (y) |
|----------|------------|
| 1 | ? |
| 5 | ? |
| 10 | ? |

- $ x = 1 $: $ y = 8(1) + 2 = 8 + 2 = 10 $
- $ x = 5 $: $ y = 8(5) + 2 = 40 + 2 = 42 $
- $ x = 10 $: $ y = 8(10) + 2 = 80 + 2 = 82 $

✔
| Input (x) | Output (y) |
|----------|------------|
| 1 | 10 |
| 5 | 42 |
| 10 | 82 |

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✔ Final Answer Summary:

Part 1:

1. Subtract 4:
- (4, 0), (16, 12), (10, 6)

2. Add 7; divide by 2:
- (1, 4), (3, 5), (5, 6)

3. Multiply by 3; add 1:
- (0, 1), (4, 13), (12, 37)

Part 2:

1. $ y = x - 5 $: (10,5), (12,7), (14,9)
2. $ y = x + 2 $: (3,5), (4,6), (5,7)
3. $ y = 4x - 3 $: (1,1), (2,5), (3,9)
4. $ y = 6x - 10 $: (6,26), (7,32), (8,38)
5. $ y = 7x + 9 $: (2,23), (3,30), (4,37)
6. $ y = 8x + 2 $: (1,10), (5,42), (10,82)

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