Determine if each mapping diagram represents a function or not.

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).
> That means:
> - Every element in the left oval (domain) must have at least one arrow (no missing mappings).
> - No element in the domain can have more than one arrow pointing to different elements in the range.

Let’s analyze each diagram one by one:

---

1)

- Domain: {0, 1, 2, 5, 6}
- Each element has one arrow.
- No element maps to more than one value.
✔ Function

---

2)

- Domain: {2, 3, 4, 6, 9}
- Check each:
- 2 → 0
- 3 → 4 and 6 → both 0 and 4? Wait:
- 3 → 0
- 4 → 4
- 6 → 0 and 4? No — wait, let's look carefully:
- 6 → 0 and 6 → 4? Yes! There are two arrows from 6: one to 0 and one to 4.
✘ Not a Function (One input maps to two outputs)

---

3)

- Domain: {2, 8, 9}
- All map to 5 only.
- Even though multiple inputs go to same output, that’s fine.
✔ Function

---

4)

- Domain: {0, 1, 4, 9}
- Check:
- 0 → 2 and 3? Two arrows from 0 → 2 and 3 → yes!
- So, 0 maps to two values: 2 and 3.
✘ Not a Function

---

5)

- Domain: {1, 2, 4, 5, 9}
- Each has exactly one arrow.
- No duplicates.
✔ Function

---

6)

- Domain: {0, 6, 8}
- All three map to 6.
- Multiple inputs → same output: allowed.
✔ Function

---

7)

- Domain: {1, 2, 8}
- Each has one arrow:
- 1 → 0
- 2 → 5
- 8 → 9
- Only one arrow per input.
✔ Function

---

8)

- Domain: {0, 2, 4, 7}
- Check:
- 0 → 3
- 2 → 6
- 4 → 6
- 7 → 9
- Each input has only one arrow.
- Multiple inputs (2 and 4) map to 6 — allowed.
✔ Function

---

✔ Final Answers:

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

---

🔍 Summary Rule:

> A mapping is a function if every input has exactly one output.
> If any input has more than one output, it's not a function.

Let me know if you'd like this formatted as a printable answer sheet!