https://file.aiquickdraw.com/mathbot/file/1725564112644ordil2s1.jpg

Let's analyze the graph and the question.

From the image:
- **Domain (D)**: The domain is the set of all possible \( x \)-values where the graph exists. The graph shows two line segments. One segment exists between \( x = -3 \) and \( x = 0 \), while the other segment exists between \( x = 2 \) and \( x = 4 \). Therefore, the domain is \( x \in [-3, 0] \cup [2, 4] \).
  
- **Range (R)**: The range is the set of all possible \( y \)-values that the graph can take. For the first segment, the \( y \)-values range from \( y = -2 \) to \( y = -1 \), and for the second segment, the \( y \)-values range from \( y = 1 \) to \( y = 2 \). Therefore, the range is \( y \in [-2, -1] \cup [1, 2] \).

The correct answer would be:
- \( D = \{ x | -3 \leq x \leq 0 \text{ or } 2 \leq x \leq 4 \} \) or \( [-3, 0] \cup [2, 4] \)
- \( R = \{ y | -2 \leq y \leq -1 \text{ or } 1 \leq y \leq 2 \} \) or \( [-2, -1] \cup [1, 2] \)

This matches with option **C**.

Would you like further details or have any other questions?

Here are 5 related questions:
1. What is the difference between domain and range in a function?
2. How can you identify the domain and range from a graph?
3. What are the common notations used for expressing domain and range?
4. What do union symbols (e.g., \( \cup \)) mean in interval notation?
5. How does set-builder notation differ from interval notation?

**Tip**: When identifying the domain and range from a graph, always look at the extreme values on both the x-axis and y-axis for the portions where the graph is defined.

Write the domain and range of the graph in set-builder and interval notation.

Understand how to determine the domain and range from line graph segments using set-builder and interval notations. This guide is tailored for high school students in grades 9-12, providing clear examples and explanations.

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