The question asks for the range of the function $g(x)$, and the graph of $g(x)$ is provided.

Observations:

• As $x \to -\infty$, the graph approaches but never reaches $y = -3$.
• As $x \to 0^+$ (from the right), the graph approaches $y = +\infty$.
• The graph has a vertical asymptote at $x = 0$.
• As $x \to 0^-$ (from the left), the graph approaches $y = -4$ but doesn't include $y = -4$ (as there's a hollow circle indicating an excluded value).
• The graph decreases as $x$ becomes negative but doesn't reach below $y = -3$.

Range:

• The function approaches all values from $-\infty$ up to but not including $y = -4$, and from $y = -3$ upwards to $\infty$, excluding $y = -3$ and $y = -4$.

Thus, the range of $g(x)$ is: $(-\infty, -4) \cup (-3, +\infty)$

This corresponds to option A: $\{ y \in \mathbb{R} \, | \, y \neq -4, -3 \}$.

Would you like more details on how to interpret this? Here are 5 related questions:

1. What is the definition of a function's range?
2. How do vertical asymptotes affect the range of a function?
3. Why are certain values like $y = -4$ and $y = -3$ excluded from the range?
4. Can you explain how to find asymptotes from a graph?
5. What are some common types of discontinuities in functions?

Tip: When analyzing a graph, always check for asymptotes and points where the function is undefined to correctly determine the range.