https://file.aiquickdraw.com/mathbot/file/1729029488628apx873uf.jpg

Let's solve this step by step:

1. **Domain**: The domain of a relation is the set of all the first elements (x-coordinates) in each ordered pair. From the given set:
   \[
   \{(-3, 0), (2, 0), (-3, 8), (-7, -8)\}
   \]
   The domain is:
   \[
   \{-3, 2, -7\}
   \]
   Notice that "-3" appears twice, but we list it only once.

2. **Range**: The range of a relation is the set of all the second elements (y-coordinates) in each ordered pair. From the given set:
   \[
   \{0, 0, 8, -8\}
   \]
   The range is:
   \[
   \{0, 8, -8\}
   \]

3. **Determine if the relation is a function**: A relation is a function if each element in the domain is paired with exactly one element in the range. In the set given, the x-coordinate "-3" is associated with two different y-values (0 and 8). This violates the definition of a function.

   Therefore, **the relation is not a function**.

### Summary:
- **Domain**: \(\{-3, 2, -7\}\)
- **Range**: \(\{0, 8, -8\}\)
- **Is it a function?**: No, it is not a function.

Would you like any further details or explanations?

### Follow-up Questions:
1. What is the difference between a function and a general relation?
2. How can we determine if a set of ordered pairs represents a one-to-one function?
3. Can a function have the same y-value for different x-values? Explain.
4. What is the significance of the domain in real-world applications?
5. How would you graph this relation on a coordinate plane?

### Tip:
To check if a set of ordered pairs is a function, remember that each input (x-value) must map to only one output (y-value). If an x-value repeats with different y-values, it's not a function.

Find the domain and the range of the relation. Determine whether the relation is a function. {(−3,0),(2,0),(−3,8),(−7,−8)}

This problem involves finding the domain and range of a given relation, and determining if the relation is a function. The relation consists of ordered pairs such as (−3,0), (2,0), (−3,8), and (−7,−8).

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