The problem shown in the image asks for the domain of a function based on the given graph. The domain refers to the set of all possible input values (typically the $x$-values) for which the function is defined.

From the graph:

• The left part of the graph shows a curve starting at $x = -6$ and going to $x = -1$, but it is open at $x = -1$, meaning $x = -1$ is not included in the domain.
• There is a gap between $x = -1$ and $x = 0$ where the function is not defined.
• The function resumes at $x = 0$ and continues to $x = 6$, including both $x = 0$ and $x = 6$.

Thus, the domain of the function in interval notation is:

$(-6, -1) \cup [0, 6]$

This indicates that the function is defined for all $x$-values between $-6$ and $-1$ (not including $-1$) and between $0$ and $6$ (including both $0$ and $6$).

Would you like further explanation on how the domain was determined, or do you have any other questions?

Here are 5 questions that might help you explore more:

1. How do you find the domain from a graph?
2. What is interval notation, and how does it work?
3. What are the key differences between open and closed intervals in domain notation?
4. How does the behavior of the function at $x = -1$ affect the domain?
5. Could there be different types of functions where gaps in the domain appear for other reasons?

Tip: Always check if a graph has any gaps, vertical asymptotes, or points where the function is undefined, as these will directly impact the domain.