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find the range and domain using set-builder notaion 

The image provided shows a line segment that starts at a point in the second quadrant and ends in the first quadrant. Let's determine the domain and range using set-builder notation.

### **Domain:**
The domain refers to all possible \( x \)-values that the line segment covers.

- The line starts at a point with a negative \( x \)-value (let's approximate this to be around \( x = -2 \)) and ends at a point with a positive \( x \)-value (around \( x = 2 \)).

**Domain in Set-Builder Notation:**
\[ \{ x \mid -2 \leq x \leq 2 \} \]
This indicates that \( x \) ranges from \(-2\) to \(2\), inclusive.

### **Range:**
The range refers to all possible \( y \)-values that the line segment covers.

- The line starts at a lower \( y \)-value (which seems to be around \( y = 1 \)) and goes up to a higher \( y \)-value (approximately \( y = 4 \)).

**Range in Set-Builder Notation:**
\[ \{ y \mid 1 \leq y \leq 4 \} \]
This means that \( y \) ranges from \(1\) to \(4\), inclusive.

**Summary:**
- **Domain:** \( \{ x \mid -2 \leq x \leq 2 \} \)
- **Range:** \( \{ y \mid 1 \leq y \leq 4 \} \)

Would you like further details or have any questions?

Here are 5 questions that expand on this topic:

1. How would the domain and range change if the line segment were extended infinitely in both directions?
2. What are the coordinates of the endpoints of the line segment?
3. How does the slope of the line segment affect the domain and range?
4. Can you find the midpoint of the line segment from the graph?
5. How would the graph change if the line segment were rotated 90 degrees?

**Tip:** To accurately describe the domain and range, carefully observe the endpoints and slopes in the graph. This practice helps in understanding the behavior of functions in different intervals.

Learn how to determine the domain and range of a line segment using set-builder notation. This problem involves analyzing a graphical representation to establish the possible x-values (domain) and y-values (range) covered by the line segment. Suitable for students in Grades 9-12 studying set theory and coordinate geometry.

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