Function Table Worksheet: Complete the table for each given function.

Let's solve each function table step by step. For each function, we'll plug in the given values of $ x $ into the function $ f(x) $ to find the corresponding $ f(x) $ values.

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1) $ f(x) = 5x^2 $

We calculate $ f(x) = 5 \times x^2 $

| $ x $ | -3 | -1 | 2 | 3 | 5 |
|--------|----|----|---|---|---|
| $ f(x) $ | $ 5(-3)^2 = 5(9) = 45 $ | $ 5(-1)^2 = 5(1) = 5 $ | $ 5(2)^2 = 5(4) = 20 $ | $ 5(3)^2 = 5(9) = 45 $ | $ 5(5)^2 = 5(25) = 125 $ |

✔ Answer: 45, 5, 20, 45, 125

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2) $ f(x) = x - 3 $

| $ x $ | 1 | 2 | 4 | 5 | 8 |
|--------|---|---|---|---|---|
| $ f(x) $ | $ 1 - 3 = -2 $ | $ 2 - 3 = -1 $ | $ 4 - 3 = 1 $ | $ 5 - 3 = 2 $ | $ 8 - 3 = 5 $ |

✔ Answer: -2, -1, 1, 2, 5

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3) $ f(x) = 2x + 4 $

| $ x $ | -2 | -1 | 1 | 2 | 5 |
|--------|----|----|---|---|---|
| $ f(x) $ | $ 2(-2) + 4 = -4 + 4 = 0 $ | $ 2(-1) + 4 = -2 + 4 = 2 $ | $ 2(1) + 4 = 2 + 4 = 6 $ | $ 2(2) + 4 = 4 + 4 = 8 $ | $ 2(5) + 4 = 10 + 4 = 14 $ |

✔ Answer: 0, 2, 6, 8, 14

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4) $ f(x) = 2x^3 $

| $ x $ | -2 | -1 | 1 | 2 | 3 |
|--------|----|----|---|---|---|
| $ f(x) $ | $ 2(-2)^3 = 2(-8) = -16 $ | $ 2(-1)^3 = 2(-1) = -2 $ | $ 2(1)^3 = 2(1) = 2 $ | $ 2(2)^3 = 2(8) = 16 $ | $ 2(3)^3 = 2(27) = 54 $ |

✔ Answer: -16, -2, 2, 16, 54

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5) $ f(x) = 3 - 2x $

| $ x $ | -3 | -1 | 0 | 2 | 3 |
|--------|----|----|---|---|---|
| $ f(x) $ | $ 3 - 2(-3) = 3 + 6 = 9 $ | $ 3 - 2(-1) = 3 + 2 = 5 $ | $ 3 - 2(0) = 3 $ | $ 3 - 2(2) = 3 - 4 = -1 $ | $ 3 - 2(3) = 3 - 6 = -3 $ |

✔ Answer: 9, 5, 3, -1, -3

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6) $ f(x) = -x^2 $

Note: This is $ -(x^2) $, not $ (-x)^2 $

| $ x $ | -4 | -3 | 0 | 1 | 2 |
|--------|----|----|---|---|---|
| $ f(x) $ | $ -(-4)^2 = -(16) = -16 $ | $ -(-3)^2 = -(9) = -9 $ | $ -(0)^2 = 0 $ | $ -(1)^2 = -1 $ | $ -(2)^2 = -4 $ |

✔ Answer: -16, -9, 0, -1, -4

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7) $ f(x) = -4 - x $

This is equivalent to $ f(x) = -x - 4 $

| $ x $ | -4 | -1 | 2 | 6 | 8 |
|--------|----|----|---|---|---|
| $ f(x) $ | $ -4 - (-4) = -4 + 4 = 0 $ | $ -4 - (-1) = -4 + 1 = -3 $ | $ -4 - 2 = -6 $ | $ -4 - 6 = -10 $ | $ -4 - 8 = -12 $ |

✔ Answer: 0, -3, -6, -10, -12

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8) $ f(x) = 8 - 5x $

| $ x $ | -6 | -3 | 0 | 3 | 5 |
|--------|----|----|---|---|---|
| $ f(x) $ | $ 8 - 5(-6) = 8 + 30 = 38 $ | $ 8 - 5(-3) = 8 + 15 = 23 $ | $ 8 - 5(0) = 8 $ | $ 8 - 5(3) = 8 - 15 = -7 $ | $ 8 - 5(5) = 8 - 25 = -17 $ |

✔ Answer: 38, 23, 8, -7, -17

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9) $ f(x) = \frac{x}{3} $

| $ x $ | -6 | -3 | 3 | 6 | 9 |
|--------|----|----|---|---|---|
| $ f(x) $ | $ \frac{-6}{3} = -2 $ | $ \frac{-3}{3} = -1 $ | $ \frac{3}{3} = 1 $ | $ \frac{6}{3} = 2 $ | $ \frac{9}{3} = 3 $ |

✔ Answer: -2, -1, 1, 2, 3

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10) $ f(x) = \frac{x^3}{2} $

| $ x $ | -2 | -1 | 1 | 2 | 4 |
|--------|----|----|---|---|---|
| $ f(x) $ | $ \frac{(-2)^3}{2} = \frac{-8}{2} = -4 $ | $ \frac{(-1)^3}{2} = \frac{-1}{2} = -0.5 $ | $ \frac{(1)^3}{2} = \frac{1}{2} = 0.5 $ | $ \frac{(2)^3}{2} = \frac{8}{2} = 4 $ | $ \frac{(4)^3}{2} = \frac{64}{2} = 32 $ |

✔ Answer: -4, -0.5, 0.5, 4, 32

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11) $ f(x) = x - 1 $

| $ x $ | -1 | 1 | 3 | 7 | 11 |
|--------|----|---|---|---|----|
| $ f(x) $ | $ -1 - 1 = -2 $ | $ 1 - 1 = 0 $ | $ 3 - 1 = 2 $ | $ 7 - 1 = 6 $ | $ 11 - 1 = 10 $ |

✔ Answer: -2, 0, 2, 6, 10

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12) $ f(x) = -3x + 7 $

| $ x $ | -5 | -1 | 0 | 5 | 7 |
|--------|----|----|---|---|---|
| $ f(x) $ | $ -3(-5) + 7 = 15 + 7 = 22 $ | $ -3(-1) + 7 = 3 + 7 = 10 $ | $ -3(0) + 7 = 7 $ | $ -3(5) + 7 = -15 + 7 = -8 $ | $ -3(7) + 7 = -21 + 7 = -14 $ |

✔ Answer: 22, 10, 7, -8, -14

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✔ Final Answer Summary:

1. 45, 5, 20, 45, 125
2. -2, -1, 1, 2, 5
3. 0, 2, 6, 8, 14
4. -16, -2, 2, 16, 54
5. 9, 5, 3, -1, -3
6. -16, -9, 0, -1, -4
7. 0, -3, -6, -10, -12
8. 38, 23, 8, -7, -17
9. -2, -1, 1, 2, 3
10. -4, -0.5, 0.5, 4, 32
11. -2, 0, 2, 6, 10
12. 22, 10, 7, -8, -14

You can now fill these values into the table on the worksheet.

Let me know if you'd like a printable version or help with graphing any of these functions!