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The worksheet you provided includes tasks for plotting relations and determining if they represent functions, as well as finding their domains and ranges. Here's how we approach each of the given problems:

### Problem 10: Relation \(\{(3, 8), (5, 7), (7, 7), (8, 9)\}\)
1. **Is it a function?**  
   To determine if it's a function, each \(x\)-value should map to exactly one \(y\)-value. Here, no two ordered pairs have the same \(x\)-value with different \(y\)-values. Therefore, this is **a function**.
   
2. **Domain**: The domain consists of all the \(x\)-values:
   \[
   \{3, 5, 7, 8\}
   \]
   
3. **Range**: The range consists of all the \(y\)-values:
   \[
   \{8, 7, 9\}
   \]

---

### Problem 11: Relation \(\{(0, 0.4), (1, 0.8), (2, 1.2), (3, 1.6)\}\)
1. **Is it a function?**  
   Each \(x\)-value corresponds to a unique \(y\)-value, so this is **a function**.
   
2. **Domain**: The domain consists of all the \(x\)-values:
   \[
   \{0, 1, 2, 3\}
   \]
   
3. **Range**: The range consists of all the \(y\)-values:
   \[
   \{0.4, 0.8, 1.2, 1.6\}
   \]

---

### Problem 12: Relation \(\{(5, -4), (3, -5), (4, -3), (6, 4)\}\)
1. **Is it a function?**  
   Each \(x\)-value corresponds to a unique \(y\)-value, so this is **a function**.
   
2. **Domain**: The domain consists of all the \(x\)-values:
   \[
   \{3, 4, 5, 6\}
   \]
   
3. **Range**: The range consists of all the \(y\)-values:
   \[
   \{-5, -4, -3, 4\}
   \]

---

### Problem 13: Relation \(\{(0.3, 0.6), (0.4, 0.8), (0.3, 0.7), (0.5, 0.5)\}\)
1. **Is it a function?**  
   Notice that the \(x\)-value 0.3 corresponds to two different \(y\)-values: 0.6 and 0.7. Therefore, this is **not a function**.
   
2. **Domain**: The domain consists of all the \(x\)-values:
   \[
   \{0.3, 0.4, 0.5\}
   \]
   
3. **Range**: The range consists of all the \(y\)-values:
   \[
   \{0.6, 0.7, 0.8, 0.5\}
   \]

---

Would you like more details or have any questions? Here are some related questions to extend your understanding:

1. What is the definition of a function in mathematical terms?
2. How would you graphically represent each of these relations?
3. What is the significance of the domain and range for real-world applications?
4. How can you identify a function just by looking at its graph?
5. Why is it important for each \(x\)-value to map to only one \(y\)-value in a function?

**Tip:** When checking if a relation is a function using a graph, the "vertical line test" is a quick way to see if any vertical line intersects the graph at more than one point. If it does, it's not a function.

Plot each of the following relations. Determine if the relation is a function and state the domain and range.

Learn how to determine if a relation is a function by using the vertical line test. This problem covers plotting relations, identifying functions, and finding domains and ranges. Suitable for students in Grades 7-9.

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