https://file.aiquickdraw.com/mathbot/file/17271907188472tlw957n.jpg

To solve this, we need to analyze the graph and determine the **domain** and **range** of the line segment. Here's how to approach it:

### Domain:
- The domain represents the set of all possible **x-values** on the graph.
- In the graph, the line segment starts at \( x = -3 \) and ends at \( x = 4 \).
- The point at \( x = -3 \) is an open circle, meaning \( x = -3 \) is **not included**.
- The point at \( x = 4 \) is a closed circle, meaning \( x = 4 \) is **included**.

Thus, the **domain** in:
- **Interval notation**: \( (-3, 4] \)
- **Set builder notation**: \( \{ x \mid -3 < x \leq 4 \} \)

### Range:
- The range represents the set of all possible **y-values** on the graph.
- The line segment starts at \( y = -3 \) (corresponding to \( x = -3 \)) and ends at \( y = -2 \) (corresponding to \( x = 4 \)).
- As before, the point at \( y = -3 \) is not included (open circle), and the point at \( y = -2 \) is included (closed circle).

Thus, the **range** in:
- **Interval notation**: \( (-3, -2] \)
- **Set builder notation**: \( \{ y \mid -3 < y \leq -2 \} \)

### Final Answers:
- **Domain (interval notation)**: \( (-3, 4] \)
- **Domain (set builder form)**: \( \{ x \mid -3 < x \leq 4 \} \)
- **Range (interval notation)**: \( (-3, -2] \)
- **Range (set builder form)**: \( \{ y \mid -3 < y \leq -2 \} \)

Would you like further clarification on these steps?

### Related Questions:
1. How is domain different from range in mathematical terms?
2. How can we determine whether a point on a graph should be included or excluded in the domain/range?
3. What are the implications of open and closed circles on graphs when defining intervals?
4. Can a function have more than one range for a given domain?
5. How do different types of graphs (e.g., parabolas, hyperbolas) affect domain and range?

### Tip:
Always carefully observe whether a point is open or closed on a graph, as this affects the inclusion or exclusion of boundary points in interval notation.

Determine the domain and range for the graph below. Write your answer in interval notation and in set builder form using a compound inequality.

Learn how to determine the domain and range of a graph and express them in both interval notation and set builder form. This problem demonstrates how to identify boundary points using inequalities.

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