To find the domain and range of the function based on the graph:

Domain:

The domain consists of all possible $x$-values that the function covers.

• The graph starts at $x = -9$ (filled circle), meaning $x = -9$ is included.
• The graph ends at $x = 9$ (filled circle), meaning $x = 9$ is also included.
• There is a break from $x = -4$ to $x = 3$ where no points are defined. This creates two intervals: from $x = -9$ to $x = -4$ (inclusive) and from $x = 3$ to $x = 9$ (inclusive).

So, the domain is $[-9, -4] \cup [3, 9]$, which matches option B.

Range:

The range consists of all possible $y$-values that the function takes.

• The lowest $y$-value is $-7$ (at $x = 6$).
• The highest $y$-value is $9$ (at $x = 9$).

Therefore, the range is $[-7, 9]$, which corresponds to option C.

Let me know if you need further clarification or details!

Related Questions:

1. How would the domain change if there were more gaps in the graph?
2. Can a function have an unbounded range but a bounded domain?
3. How do filled and unfilled circles affect domain and range?
4. What are examples of functions with all real numbers as their domain?
5. How can we express the union of intervals in set notation?

Tip: Always pay attention to filled versus unfilled circles in graphs to determine inclusivity for domain and range.