Worksheet on identifying functions using domain and range mapping diagrams.

To determine whether each mapping diagram represents a function, we use the definition of a function:

> A function is a relation where each input (element in the domain) is associated with exactly one output (element in the range).
> In other words, no element in the domain can map to more than one element in the range.

We will examine each diagram and check if any input (left oval) maps to more than one output (right oval). If yes → Not a Function. If no → Function.

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1)

- Domain: {0, 1, 2, 5, 6}
- Each element maps to only one value in the range.
- For example:
- 0 → 5
- 1 → 7
- 2 → 6
- 5 → 8
- 6 → 8
- ✔ All inputs have one unique output
- Answer: Function

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2)

- Domain: {2, 3, 4, 6, 9}
- Check each:
- 2 → 0
- 3 → 4
- 4 → 6
- 6 → 0 and 4 → two outputs? Wait:
- 6 → 0 and 6 → 4 → Two outputs!
- So 6 maps to both 0 and 4 → ✘ Not allowed!
- Answer: Not a Function

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3)

- Domain: {2, 8, 9}
- 2 → 5
- 8 → 5
- 9 → 5
- All inputs map to only one output (5), even though multiple inputs go to same output — that’s fine.
- ✔ One output per input
- Answer: Function

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4)

- Domain: {0, 1, 4, 9}
- Check each:
- 0 → 2
- 1 → 8
- 4 → 3
- 9 → 9
- Each input has only one arrow → ✔
- Answer: Function

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5)

- Domain: {1, 2, 4, 5, 9}
- 1 → 2
- 2 → 3
- 4 → 7
- 5 → 9
- 9 → 3
- All inputs have exactly one output → ✔
- Answer: Function

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6)

- Domain: {0, 6, 8}
- 0 → 5
- 6 → 6
- 8 → 6
- All inputs map to one output → ✔
- Even though 6 and 8 both map to 6, that's okay.
- Answer: Function

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7)

- Domain: {1, 2, 8}
- 1 → 0
- 2 → 5
- 8 → 9
- All inputs have only one output → ✔
- Answer: Function

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8)

- Domain: {0, 2, 4, 7}
- 0 → 3
- 2 → 6
- 4 → 9
- 7 → 6
- Each input has one output → ✔
- Answer: Function

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Final Answers:

1) Function
2) Not a Function
3) Function
4) Function
5) Function
6) Function
7) Function
8) Function

✔ Only #2 fails because 6 maps to both 0 and 4.

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Summary:

| # | Answer |
|---|----------------|
| 1 | Function |
| 2 | Not a Function |
| 3 | Function |
| 4 | Function |
| 5 | Function |
| 6 | Function |
| 7 | Function |
| 8 | Function |

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