The image shows a graph of a function with its domain being asked. To determine the domain of the function, we need to observe the x-values for which the function is defined.

Analyzing the Graph:

1. Left side of the graph: The function starts from the left, where the x-values extend to negative infinity.

2. Intervals of x-values where the function is defined:

   • The function is continuous from $-\infty$ up to $x = -2$ (marked with a filled circle at $(-2, 4)$).
   • There is a gap in the function from $x = -2$ to $x = -1$. The function resumes at $x = -1$ (again, marked with a filled circle at $(-1, 2)$), and continues to $x = 3$.
   • The function is defined for $x = 3$ to $\infty$ with no interruptions.

3. Intervals where the function is not defined:

   • Between $x = -2$ and $x = -1$, the function is not defined.
   • The function is defined again from $x = -1$ to $x = 3$ and resumes at $x = 3$ extending to infinity.

The Domain:

• The domain of the function includes all x-values except for the interval where the function is not defined, i.e., from $-2$ to $-1$.

So, the correct answer is: $\boxed{(-\infty, -2] \cup [-1, 3) \cup [3, \infty)}$

Do you want more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How would the domain change if the open circle at $x = -2$ were a closed circle?
2. What is the range of the function as shown in the graph?
3. How can you determine the domain if the graph is not provided, but the function is given algebraically?
4. If the function had been continuous without any gaps, what would its domain be?
5. How do you determine the domain for piecewise functions?

Tip: Always pay close attention to open and closed circles in graphs, as they indicate whether specific points are included in the domain or not.