Comparing Linear, Exponential, and Quadratic Functions Worksheets ... - Free Printable

Let's solve each problem by analyzing the patterns in the tables to determine whether the function is linear, exponential, or quadratic.

We'll use these rules:

- Linear: The first differences (changes in y) are constant.
- Exponential: The ratios of consecutive y-values are constant (if x increases by a constant amount).
- Quadratic: The second differences (differences of the first differences) are constant.

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1.

| x | 2 | 4 | 6 | 8 | 10 |
|---|---|---|---|---|----|
| y | 12| 0 |-4 | 0 | 12 |

First differences:
- 0 - 12 = -12
- -4 - 0 = -4
- 0 - (-4) = 4
- 12 - 0 = 12

→ Not constant → not linear
Now check second differences:
- -4 - (-12) = 8
- 4 - (-4) = 8
- 12 - 4 = 8

→ Second differences are constant (8) → Quadratic

✔ Answer: Quadratic

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2.

| x | -2 | -1 | 0 | 1 | 2 |
|---|----|----|---|---|---|
| y | 1 | 2 | 4 | 8 | 16|

Ratios of y-values:
- 2/1 = 2
- 4/2 = 2
- 8/4 = 2
- 16/8 = 2

→ Constant ratio = 2 → Exponential

✔ Answer: Exponential

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3.

| x | -3 | -2 | -1 | 0 | 1 |
|---|----|----|----|---|---|
| y | 11 | 8 | 5 | 2 | -1|

First differences:
- 8 - 11 = -3
- 5 - 8 = -3
- 2 - 5 = -3
- -1 - 2 = -3

→ Constant difference = -3 → Linear

✔ Answer: Linear

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4.

| x | -2 | -1 | 0 | 1 | 2 |
|---|----|----|---|---|---|
| y | -2 | 1 | 4 | 7 | 10|

First differences:
- 1 - (-2) = 3
- 4 - 1 = 3
- 7 - 4 = 3
- 10 - 7 = 3

→ Constant difference = 3 → Linear

✔ Answer: Linear

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5.

| x | -2 | -1 | 0 | 1 | 2 |
|---|----|----|---|---|---|
| y | -6 | -6 | -4 | 0 | 6 |

First differences:
- -6 - (-6) = 0
- -4 - (-6) = 2
- 0 - (-4) = 4
- 6 - 0 = 6

→ Not constant → not linear
Second differences:
- 2 - 0 = 2
- 4 - 2 = 2
- 6 - 4 = 2

→ Constant second differences = 2 → Quadratic

✔ Answer: Quadratic

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6.

| x | -2 | -1 | 0 | 1 |
|---|----|----|---|---|
| y | 0.08 | 0.4 | 2 | 10 |

Ratios:
- 0.4 / 0.08 = 5
- 2 / 0.4 = 5
- 10 / 2 = 5

→ Constant ratio = 5 → Exponential

✔ Answer: Exponential

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7.

| x | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| y | 3 | 2 | 3 | 6 | 11 |

First differences:
- 2 - 3 = -1
- 3 - 2 = 1
- 6 - 3 = 3
- 11 - 6 = 5

→ Not constant
Second differences:
- 1 - (-1) = 2
- 3 - 1 = 2
- 5 - 3 = 2

→ Constant second differences = 2 → Quadratic

✔ Answer: Quadratic

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8.

| x | -3 | -2 | -1 | 0 | 1 |
|---|----|----|----|---|---|
| y | 4 | 0 | -2 | -2 | 0 |

First differences:
- 0 - 4 = -4
- -2 - 0 = -2
- -2 - (-2) = 0
- 0 - (-2) = 2

→ Not constant
Second differences:
- -2 - (-4) = 2
- 0 - (-2) = 2
- 2 - 0 = 2

→ Constant second differences = 2 → Quadratic

✔ Answer: Quadratic

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9.

| x | 0 | 2 | 1 | -1 | -2 |
|---|---|---|---|----|----|
| y | 2 | 8 | 4 | 1 | 0.5 |

Note: x-values are not ordered, so let's reorder them by x:

Reorder:
| x | -2 | -1 | 0 | 1 | 2 |
|---|----|----|---|---|---|
| y | 0.5 | 1 | 2 | 4 | 8 |

Now check ratios:
- 1 / 0.5 = 2
- 2 / 1 = 2
- 4 / 2 = 2
- 8 / 4 = 2

→ Constant ratio = 2 → Exponential

✔ Answer: Exponential

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10.

| x | 0 | 2 | 4 | -2 | -4 |
|---|---|---|---|----|----|
| y | 1 | 4 | 7 | -2 | -5 |

Reorder by x:
| x | -4 | -2 | 0 | 2 | 4 |
|---|----|----|---|---|---|
| y | -5 | -2 | 1 | 4 | 7 |

First differences:
- -2 - (-5) = 3
- 1 - (-2) = 3
- 4 - 1 = 3
- 7 - 4 = 3

→ Constant difference = 3 → Linear

✔ Answer: Linear

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✔ Final Answers:

1. Quadratic
2. Exponential
3. Linear
4. Linear
5. Quadratic
6. Exponential
7. Quadratic
8. Quadratic
9. Exponential
10. Linear

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Let me know if you'd like the equations for any of them!