Printable math worksheet featuring six problems where students must analyze tables of x and y values to determine if each relation is a function.

To determine whether each table of values represents a function, we need to check if each input \( x \) corresponds to exactly one output \( y \). This is the definition of a function: for every element in the domain (input), there must be exactly one corresponding element in the range (output).

Let's analyze each table step by step:

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Table 1

| \( x \) | \( y \) |
|---------|---------|
| -2 | 2 |
| 0 | 16 |
| 3 | -6 |
| 5 | -15 |

- Each \( x \)-value appears only once.
- There are no repeated \( x \)-values with different \( y \)-values.
- Therefore, this table represents a function.

Conclusion for Table 1: It is a function.

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Table 2

| \( x \) | \( y \) |
|---------|---------|
| -9 | -18 |
| -12 | -24 |
| -17 | 16 |
| 11 | 11 |

- Each \( x \)-value appears only once.
- There are no repeated \( x \)-values with different \( y \)-values.
- Therefore, this table represents a function.

Conclusion for Table 2: It is a function.

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Table 3

| \( x \) | \( y \) |
|---------|---------|
| 4 | -20 |
| -17 | -17 |
| 16 | 3 |
| 0 | -16 |

- Each \( x \)-value appears only once.
- There are no repeated \( x \)-values with different \( y \)-values.
- Therefore, this table represents a function.

Conclusion for Table 3: It is a function.

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Table 4

| \( x \) | \( y \) |
|---------|---------|
| -15 | 18 |
| -15 | -18 |
| -19 | -18 |
| -18 | -18 |

- The \( x \)-value \(-15\) appears twice, but it corresponds to two different \( y \)-values (\( 18 \) and \(-18\)).
- This violates the definition of a function, as one input cannot have multiple outputs.
- Therefore, this table does not represent a function.

Conclusion for Table 4: It is not a function.

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Table 5

| \( x \) | \( y \) |
|---------|---------|
| 2 | 15 |
| 0 | 15 |
| 4 | 15 |
| 2 | -15 |

- The \( x \)-value \( 2 \) appears twice, but it corresponds to two different \( y \)-values (\( 15 \) and \(-15\)).
- This violates the definition of a function, as one input cannot have multiple outputs.
- Therefore, this table does not represent a function.

Conclusion for Table 5: It is not a function.

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Table 6

| \( x \) | \( y \) |
|---------|---------|
| -13 | -3 |
| -12 | -3 |
| -12 | -12 |
| -5 | 94 |

- The \( x \)-value \(-12\) appears twice, but it corresponds to two different \( y \)-values (\( -3 \) and \(-12\)).
- This violates the definition of a function, as one input cannot have multiple outputs.
- Therefore, this table does not represent a function.

Conclusion for Table 6: It is not a function.

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Final Answer

Summarizing the conclusions for all tables:
1. Function
2. Function
3. Function
4. Not a function
5. Not a function
6. Not a function

$$
\boxed{\text{Function, Function, Function, Not a function, Not a function, Not a function}}
$$