To determine the correct inequality representing the domain of the function shown in the graph, let's analyze it step by step:

The domain of a function represents the set of all possible x-values that the function can take. By inspecting the graph:

1. The line begins at x = -3 and ends at x = 6.
2. Both points at $x = -3$ and $x = 6$ are filled in, indicating that the endpoints are included in the domain.

Thus, the domain includes all values of $x$ from $-3$ to $6$, including both endpoints.

The inequality that best represents this domain is:

$\boxed{-3 \leq x \leq 6}$ So the correct answer is Option A.

Would you like more details on how domains are determined from graphs?

Here are 5 related questions to explore:

1. What is the range of the function shown on the graph?
2. How can you determine if a function is continuous from its graph?
3. What happens to the domain of a function if the endpoints are open circles?
4. How would the inequality change if the line extended beyond $x = 6$?
5. Can a function have multiple domain restrictions in one graph?

Tip: Always check whether the endpoints of a function's graph are open (excluded) or closed (included) when determining the domain.