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.