To sketch the transformation of the function $-f(x+4) - 3$ on the same grid, we need to apply the following steps:

1. Horizontal Shift: The term $f(x+4)$ represents a left shift of the function by 4 units. This means every point on the original function moves 4 units to the left.

2. Reflection in the x-axis: The negative sign before the function $-f(x+4)$ reflects the function across the x-axis. This flips all the y-values of the points on the graph. So, if a point was at $(x, y)$, after reflection, it will be at $(x, -y)$.

3. Vertical Shift: The $-3$ represents a downward shift by 3 units. After reflecting the function, every point is shifted 3 units down.

Instructions to sketch:

1. Start by shifting the entire graph of $f(x)$ 4 units to the left.
2. Then reflect the new graph across the x-axis, flipping it upside down.
3. Finally, shift the reflected graph downward by 3 units.

Let me know if you'd like me to guide you through each step further. Would you like to see an example of one of the points transformed?

Here are 5 relative questions for further exploration:

1. How does horizontal shifting affect the shape of the graph?
2. What happens when a function is reflected over the x-axis?
3. Can you identify the transformations in terms of function composition?
4. What effect does adding or subtracting from $x$ have on the function’s behavior?
5. How can you describe the domain and range of the transformed function?

Tip: Always apply transformations step by step to avoid confusion, especially when dealing with multiple changes like shifts and reflections.