https://file.aiquickdraw.com/mathbot/file/1728729825833dwseusiw.jpg

Let's go through each part systematically. For every part, we will:

1. **List the Domain**: The set of all first components (x-values).
2. **List the Range**: The set of all second components (y-values).
3. **Check if it's a Function**: If **every x-value maps to exactly one y-value**, the relation is a function. Otherwise, it is not.

---

### (a) \(\{(-4, -3), (2, -5), (4, 6), (2, 0)\}\)
- **Domain**: \(\{-4, 2, 4\}\)
- **Range**: \(\{-3, -5, 6, 0\}\)
- **Is it a Function?**  
  **No**, because \(x = 2\) is mapped to both \(-5\) and \(0\).

---

### (b) \(\{(8, -2), (6, -\frac{3}{2}), (-1, 5)\}\)
- **Domain**: \(\{8, 6, -1\}\)
- **Range**: \(\{-2, -\frac{3}{2}, 5\}\)
- **Is it a Function?**  
  **Yes**, each x-value has a unique y-value.

---

### (c) \(\left\{(-\sqrt{3}, 3), (-1.1, 0), (0, 0), (1.1, 1.1), (\sqrt{3}, 3)\right\}\)
- **Domain**: \(\{-\sqrt{3}, -1.1, 0, 1.1, \sqrt{3}\}\)
- **Range**: \(\{3, 0, 1.1\}\)
- **Is it a Function?**  
  **No**, because both \(x = -\sqrt{3}\) and \(x = \sqrt{3}\) map to the same \(y = 3\).

---

### (d) \(\left\{\left(-\frac{1}{2}, \frac{1}{6}\right), (-1, 1), \left(\frac{1}{3}, \frac{1}{3}\right)\right\}\)
- **Domain**: \(\left\{-\frac{1}{2}, -1, \frac{1}{3}\right\}\)
- **Range**: \(\left\{\frac{1}{6}, 1, \frac{1}{3}\right\}\)
- **Is it a Function?**  
  **Yes**, each x-value maps to a unique y-value.

---

### (e) \(\{(0, 5), (1, 5), (2, 5), (3, 5), (4, 5), (5, 5)\}\)
- **Domain**: \(\{0, 1, 2, 3, 4, 5\}\)
- **Range**: \(\{5\}\)
- **Is it a Function?**  
  **Yes**, each x-value has a unique y-value (even though all map to 5).

---

### (f) \(\{(5, 0), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5)\}\)
- **Domain**: \(\{5\}\)
- **Range**: \(\{0, 1, 2, 3, 4, 5\}\)
- **Is it a Function?**  
  **No**, because \(x = 5\) maps to multiple y-values (0, 1, 2, 3, 4, 5).

---

## Summary
| Part | Domain                         | Range                       | Is it a Function? |
|------|--------------------------------|-----------------------------|-------------------|
| (a)  | \(\{-4, 2, 4\}\)               | \(\{-3, -5, 6, 0\}\)        | No                |
| (b)  | \(\{8, 6, -1\}\)               | \(\{-2, -\frac{3}{2}, 5\}\) | Yes               |
| (c)  | \(\{-\sqrt{3}, -1.1, 0, 1.1, \sqrt{3}\}\) | \(\{3, 0, 1.1\}\) | No                |
| (d)  | \(\left\{-\frac{1}{2}, -1, \frac{1}{3}\right\}\) | \(\left\{\frac{1}{6}, 1, \frac{1}{3}\right\}\) | Yes |
| (e)  | \(\{0, 1, 2, 3, 4, 5\}\)       | \(\{5\}\)                   | Yes               |
| (f)  | \(\{5\}\)                      | \(\{0, 1, 2, 3, 4, 5\}\)    | No                |

---

Do you have any further questions or want more details on specific parts?

### 5 Related Questions
1. What makes a relation not a function?
2. How is the domain different from the range?
3. Can a function have repeated y-values?
4. What is the difference between a function and a one-to-one function?
5. How do you determine the range when graphing a function?

### Tip
Always check for repeated x-values with different y-values to quickly identify whether a relation is a function.

Determine the domain and range of the given relation. Is the relation a function?

Analyze six sets of ordered pairs to determine their domains and ranges. Explore whether each relation represents a function. This exercise is ideal for students in grades 9-12 learning about functions, relations, and mapping rules.

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