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The image shows a task asking for the domain and range of a graph, with the answers to be provided both in interval notation and set-builder notation. The graph displayed is a straight line segment connecting two points: \((-4, 3)\) and \((3, -4)\).

Let's break this down:

### Domain:
The domain represents all possible \(x\)-values of the function. In this case, the \(x\)-values range from \(-4\) to \(3\), since the line segment starts at \(x = -4\) and ends at \(x = 3\).

- **Interval Notation for Domain**: 
  \[
  [-4, 3]
  \]
  (The square brackets indicate that the endpoints \(-4\) and \(3\) are included.)

- **Set-Builder Notation for Domain**:
  \[
  \{x \mid -4 \leq x \leq 3\}
  \]
  (This means \(x\) is any real number between \(-4\) and \(3\), inclusive.)

### Range:
The range represents all possible \(y\)-values of the function. The \(y\)-values span from \(y = -4\) to \(y = 3\), as the line descends from \((x = -4, y = 3)\) to \((x = 3, y = -4)\).

- **Interval Notation for Range**: 
  \[
  [-4, 3]
  \]
  (Similar to the domain, the range also includes both endpoints.)

- **Set-Builder Notation for Range**:
  \[
  \{y \mid -4 \leq y \leq 3\}
  \]
  (This means \(y\) is any real number between \(-4\) and \(3\), inclusive.)

### Summary:

- **Domain (Interval Notation)**: \([-4, 3]\)
- **Domain (Set-Builder Notation)**: \(\{x \mid -4 \leq x \leq 3\}\)
- **Range (Interval Notation)**: \([-4, 3]\)
- **Range (Set-Builder Notation)**: \(\{y \mid -4 \leq y \leq 3\}\)

Would you like any further explanation or details on this? Here are some related questions to expand your understanding:

1. How is set-builder notation different from interval notation?
2. Can a function have the same domain but different ranges?
3. How would the domain and range change if the line segment were extended?
4. What if one endpoint of the segment were excluded (e.g., an open circle)?
5. How do you find the slope of the line segment from these points?

**Tip**: Always look at the extremes of the \(x\)- and \(y\)-values in a graph to determine the domain and range!

Determine the domain and range of the given line segment graph and write your answer in both interval and set-builder notation.

Learn how to determine the domain and range of a graph representing a line segment. This problem explains how to express these values in both interval and set-builder notation, focusing on linear equations and graphing skills. Suitable for students in Grades 7-9.

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