Determine whether each mapping diagram represents a function or not.

Let's solve each of the domain and range mapping diagrams to determine whether each depicts a function or not.

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🔍 Definition of a Function:

A function is a relation where each input (element in the domain) is paired 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.
- But multiple inputs can map to the same output.

We’ll go through each diagram one by one.

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1)

Domain: {2, 6, 7, 8, 9}
Range: {0, 7, 9}

- 2 → 0
- 6 → 7
- 7 → 7
- 8 → 9
- 9 → 9

✔ Each input maps to only one output.
Even though 7 and 8 both map to 7 and 9 respectively, and multiple inputs go to same outputs — that’s fine.

➡️ Function: YES

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2)

Domain: {5, 7, 9}
Range: {1, 3, 6, 8}

- 5 → 1
- 5 → 3
- 7 → 6
- 9 → 8
- 9 → 1

✘ 5 maps to both 1 and 3, and 9 maps to both 8 and 1 → multiple outputs for single inputs.

➡️ Function: NO

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3)

Domain: {1, 3, 6}
Range: {1, 6, 7, 8, 9}

- 1 → 1
- 1 → 6
- 3 → 7
- 6 → 9

✘ 1 maps to both 1 and 6 → violates function rule.

➡️ Function: NO

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4)

Domain: {1, 2, 5, 7, 8}
Range: {1, 2, 3, 4}

- 1 → 1
- 2 → 3
- 5 → 4
- 7 → 3
- 8 → 4

✔ Each input maps to only one output.
Multiple inputs (like 2 and 7) go to 3 — allowed.

➡️ Function: YES

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5)

Domain: {0, 2, 5, 6, 7}
Range: {0, 2, 6, 8}

- 0 → 0
- 0 → 2
- 0 → 6
- 0 → 8
- 2 → 2
- 5 → 6
- 6 → 8
- 7 → 0

✘ 0 maps to four different values → not allowed.

➡️ Function: NO

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6)

Domain: {3, 4, 7}
Range: {3, 5, 8}

- 3 → 3
- 4 → 3
- 7 → 3

✔ All inputs map to only one output (even though all go to 3).

➡️ Function: YES

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7)

Domain: {4, 5, 8, 9}
Range: {0, 4, 7, 8, 9}

- 4 → 0
- 4 → 4
- 4 → 7
- 5 → 8
- 5 → 9
- 8 → 0
- 9 → 4

✘ 4 maps to 0, 4, and 7 → multiple outputs
✘ 5 maps to 8 and 9 → multiple outputs

➡️ Function: NO

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8)

Domain: {0, 1, 8, 9}
Range: {1, 2, 7}

- 0 → 1
- 1 → 2
- 8 → 7
- 9 → 1

✔ Each input has exactly one output.
Even though 0 and 9 both map to 1 — that's okay.

➡️ Function: YES

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✔ Final Answers:

| Diagram | Function? |
|--------|-----------|
| 1) | Yes |
| 2) | No |
| 3) | No |
| 4) | Yes |
| 5) | No |
| 6) | Yes |
| 7) | No |
| 8) | Yes |

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📝 Summary:

To determine if a mapping diagram is a function:
- Check if any input (left side) connects to more than one output (right side).
- If yes → Not a function.
- If no → It is a function.

✔ Only diagrams 1, 4, 6, and 8 are functions.
✘ Diagrams 2, 3, 5, and 7 are not functions due to multiple outputs from a single input.

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