Math worksheet for practicing identifying functions from various representations including tables, mapping diagrams, and ordered pairs.

Let's go through each of the 8 problems and determine whether each relation is a function.

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🔹 Definition: What is a Function?

A function is a relation where each input (x-value) has exactly one output (y-value).
In other words:
- No x-value can be paired with more than one y-value.
- If any input appears more than once with different outputs, it’s not a function.

We'll check each problem using this rule.

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✔ Problem 1:

```
x | y
5 | 1
5 | 2
5 | 3
5 | 4
```

- The same input `x = 5` maps to multiple outputs: 1, 2, 3, 4.
- ✘ Not a function (same input → multiple outputs)

> Answer: Not a function

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✔ Problem 2:

Input → Output mapping:
- 6 → 9
- 8 → 11
- 11 → 15
- 14 → 20

Each input maps to exactly one output.
Even though some outputs are shared, that’s fine — as long as inputs don’t repeat with different outputs.

- ✔️ Function

> Answer: Function

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✔ Problem 3:

Input → Output:
- -5 → 2
- -2 → 8
- 1 → 7
- 0 → 6

Wait — look closely at input = 1: it maps to 7, but also seems to map to 6?

Actually, from the diagram:
- Input 1 has two arrows: one to 7, one to 6?
Wait — let's examine:

From the diagram:
- -5 → 2
- -2 → 8
- 1 → 7
- 0 → 6

But wait: Is there a second arrow from 1 to 6?
Looking carefully: It appears that 1 has two outputs: 7 and 6.

Yes — both lines go from 1 to 7 and 1 to 6.

So:
- Input `1` → outputs `7` and `6`
- ✘ Multiple outputs for same input → Not a function

> Answer: Not a function

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✔ Problem 4:

List of ordered pairs:
(-9, 4)
(2, 8)
(0, 1)
(6, 5)
(2, 3)

Now check for repeated x-values:
- x = 2 appears twice: once with y = 8, once with y = 3

So:
- Input `2` → two different outputs → ✘ Not a function

> Answer: Not a function

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✔ Problem 5:

Table:
| x | y |
|---|---|
| 6 | -4 |
| 8 | 2 |
|10 | 6 |
|12 |-4 |
|14 |11 |

Check for repeated x-values:
- All x-values are unique: 6, 8, 10, 12, 14 → no repeats
- Each x has only one y

✔️ Function

> Answer: Function

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✔ Problem 6:

Input → Output:
- 3 → 2
- 6 → 4
- 9 → 6
- 12 → 4

All inputs are unique.
Each input maps to only one output.
Note: output 4 appears twice (from 6 and 12), but that’s allowed.

✔️ Function

> Answer: Function

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✔ Problem 7:

Ordered pairs:
(-11, 14)
(-13, 14)
(3, 12)
(1, 14)
(8, 11)

Check x-values:
- -11, -13, 3, 1, 8 → all different
- No repeated x-values → each input has one output

✔️ Function

> Answer: Function

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✔ Problem 8:

Table:
| x | y |
|----|---|
| -9 | 4 |
| -8 | 3 |
| -8 | 1 |
| -6 | 0 |
| -4 |-3 |

Look at x = -8:
- Appears twice: once with y = 3, once with y = 1
- So input `-8` has two different outputs → ✘ Not a function

> Answer: Not a function

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✔ Final Answers Summary:

| Problem | Is it a function? |
|--------|-------------------|
| 1 | ✘ No |
| 2 | ✔️ Yes |
| 3 | ✘ No |
| 4 | ✘ No |
| 5 | ✔️ Yes |
| 6 | ✔️ Yes |
| 7 | ✔️ Yes |
| 8 | ✘ No |

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✔ Explanation Recap:

- A function requires each input (x) to have only one output (y).
- If an x-value repeats with different y-values, it's not a function.
- Repeated outputs are fine.

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