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Let's solve each part of the worksheet one by one:

### 1. Ordered Pairs and Functions
We need to determine if each set of ordered pairs is a function, and then identify its domain and range.

**Problem 1:**
- Ordered pairs: \{(1, -2), (-2, 0), (-1, 2), (1, 3)\}

- **Function?**  
  No. The input \( x = 1 \) is repeated, but with different outputs (-2 and 3). This violates the rule of a function where each input must map to exactly one output.

- **Domain:**  
  \{-2, -1, 1\} (The set of all distinct \(x\)-values)

- **Range:**  
  \{-2, 0, 2, 3\} (The set of all distinct \(y\)-values)

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**Problem 2:**
- Ordered pairs: \{(1, 1), (2, 2), (3, 5), (4, 10), (5, 15)\}

- **Function?**  
  Yes. Each input (x-value) is unique and maps to exactly one output (y-value).

- **Domain:**  
  \{1, 2, 3, 4, 5\}

- **Range:**  
  \{1, 2, 5, 10, 15\}

---

**Problem 3:**
- Ordered pairs: \(\left\{ \left( 17, \frac{15}{4} \right), \left( \frac{15}{4}, 17 \right), \left( 15, \frac{17}{4} \right), \left( \frac{17}{4}, 15 \right) \right\}\)

- **Function?**  
  Yes. Each input (x-value) is unique and maps to exactly one output (y-value).

- **Domain:**  
  \{17, 15/4, 15, 17/4\}

- **Range:**  
  \{15/4, 17, 17/4, 15\}

---

**Problem 4:**
- Ordered pairs: \(\left\{ \left( -\frac{3}{5}, 2 \right), \left( -\frac{3}{5}, -\frac{3}{5} \right), \left( \frac{3}{2}, -5 \right), \left( 5, 2 \right) \right\}\)

- **Function?**  
  No. The input \( x = -\frac{3}{5} \) repeats with two different outputs (2 and -3/5), violating the function rule.

- **Domain:**  
  \{-3/5, 3/2, 5\}

- **Range:**  
  \{2, -3/5, -5\}

---

### 2. Relations Expressed as Graphing

We need to analyze each graph, identify its domain and range, and determine if it represents a function.

---

**Problem 5:**
- The points are: \((-2, 2), (0, 0), (2, 0), (0, -2)\)

- **Relation:**  
  \{(-2, 2), (0, 0), (2, 0), (0, -2)\}

- **Domain:**  
  \{-2, 0, 2\} (The set of distinct \(x\)-values)

- **Range:**  
  \{-2, 0, 2\} (The set of distinct \(y\)-values)

- **Function?**  
  No. The input \(x = 0\) maps to two different outputs (0 and -2), so it is not a function.

---

**Problem 6:**
- The points are: \((-2, -1), (-1, 0), (0, 1), (1, 2)\)

- **Relation:**  
  \{(-2, -1), (-1, 0), (0, 1), (1, 2)\}

- **Domain:**  
  \{-2, -1, 0, 1\}

- **Range:**  
  \{-1, 0, 1, 2\}

- **Function?**  
  Yes. Each input (x-value) maps to exactly one output (y-value).

---

Would you like any specific details explained further? Here are five related questions:

1. What is the formal definition of a function?
2. How do you determine the domain and range from a set of ordered pairs?
3. What are the conditions under which a relation is not a function?
4. Can a function have repeated values in the range? Why or why not?
5. How can a vertical line test be used to determine if a graph represents a function?

**Tip:** In mathematics, the domain is the set of all possible inputs (x-values), while the range is the set of all possible outputs (y-values). Always check for repeated x-values to verify if a relation is a function.

Determine if the following relations are functions, state the domain and range, and analyze the graphs.

This worksheet focuses on determining whether a given relation is a function, finding the domain and range of ordered pairs, and analyzing graphs. Suitable for students in Grades 9-11.

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