Here is the graph of the function $f(x) = -3 - \ln(x+3)$.

The graph features a vertical asymptote at $x = -3$, and as $x \to -3^+$, the function approaches positive infinity. As $x \to \infty$, the function approaches negative infinity. This graph confirms that the correct choice was Graph D from the provided options.

Would you like more details or have any questions? Here are some other questions you might want to ask:

1. How to graph a natural logarithmic function with transformations?
2. How to determine vertical asymptotes of logarithmic functions?
3. How to find the domain and range of a logarithmic function?
4. What are common properties of logarithmic functions?
5. How to calculate intercepts of logarithmic functions?

Tip: When graphing logarithmic functions, identifying the vertical asymptotes and understanding the end behavior are crucial steps for accuracy.