To determine the domain of the function $g(x)$ in the given graph, we need to identify the range of $x$-values for which the function is defined. The graph shows the following features:

1. The function $g(x)$ starts at $x = -3$ but has an open circle at this point, indicating that $g(x)$ is not defined at $x = -3$.
2. The function continues from just to the right of $x = -3$ and extends rightward indefinitely along the $x$-axis.

This information tells us:

• The function is defined for all $x$ values greater than $-3$.
• It extends to positive infinity.

Therefore, the correct domain of the function is: $x \in (-3, \infty)$

So, the correct answer is the first option:

• $x \in (-3, \infty)$

Would you like further explanation or have any questions?

Here are some related questions to expand your understanding:

1. How do you determine the range of a function given its graph?
2. What does an open circle on a graph indicate about the function at that point?
3. How does the domain differ from the range of a function?
4. What happens to the domain if there are restrictions like division by zero or square roots?
5. How would the answer change if the function was defined at $x = -3$?

Tip: When looking at a graph, always check for open or closed circles; these indicate whether endpoints are included or excluded in the domain or range.