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The problem requires identifying the domain and range of a piecewise-defined function based on its graph.

### Domain:
The **domain** of a function refers to the set of all possible input values (x-values) for which the function is defined.

Looking at the graph:
- The x-values span from **-8** to **9**, with a break between **2** and **3** where the function is not defined.

Thus, the domain consists of:
- From **-8 to 2** (inclusive of -8 and 2).
- From **3 to 9** (inclusive of 3 and 9).

This matches option **B: [-8, 2] and [3, 9]**.

### Range:
The **range** of a function refers to the set of all possible output values (y-values).

Based on the graph:
- The lowest y-value is **-6**, and the highest is **9**.
- The function covers all y-values from **-6** to **9**, without any gaps.

This matches option **B: [-6, 9]** for the range.

So, the selected answers are:
- Domain: **B. [-8, 2] and [3, 9]**
- Range: **B. [-6, 9]**

Would you like more details or explanations? 

Here are five related questions to expand your understanding:
1. What is a piecewise function, and how is it defined?
2. How do you identify breaks in the domain of a function from its graph?
3. How can the range of a function change if the graph had discontinuities?
4. Can a function have multiple ranges for different intervals of its domain?
5. What are open and closed intervals in the context of domains and ranges?

**Tip:** When analyzing a graph, always check for gaps, breaks, or undefined points to determine both domain and range accurately.

Find the domain and range of the function whose graph is on the right.

Learn how to find the domain and range of a piecewise-defined function by analyzing its graph. This problem guides you through identifying domain breaks and calculating the range based on y-values. Suitable for students in Grades 9-12.

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