To shift the graph of $f(x) = -|x|$ down by 4 units, we need to subtract 4 from the original function. This is because shifting a graph downward corresponds to subtracting a constant value from the function.

So, if $f(x) = -|x|$, then the new function $g(x)$ that shifts the graph of $f(x)$ down by 4 units is:

$g(x) = f(x) - 4$

Substituting $f(x) = -|x|$ into the equation:

$g(x) = -|x| - 4$

Thus, the equation of the function $g(x)$ is:

$g(x) = -|x| - 4$

Let me know if you need further clarification!

Here are 5 related questions to explore:

1. What happens if you shift the graph of $f(x) = -|x|$ up by 4 units instead?
2. How would you transform $f(x) = -|x|$ to reflect it across the x-axis?
3. What is the effect of shifting a graph horizontally instead of vertically?
4. How would you shift $f(x) = -|x|$ to the left by 3 units?
5. How can you modify a function to stretch or compress its graph vertically?

Tip: When shifting a graph vertically, always adjust the function by adding or subtracting the shift amount.