To shift the graph of the function $f(x) = |x|$ downward by 3 units, we simply subtract 3 from the original function. This transformation is a vertical shift downward.

So, the equation of the function $g(x)$, which represents the graph of $f(x)$ shifted downward by 3 units, will be:

$g(x) = |x| - 3$

This means that every point on the graph of $f(x) = |x|$ is moved down by 3 units to create the new graph of $g(x)$.

Let me know if you'd like further details or if you have any questions!

Here are 5 related questions:

1. What happens to the graph of $f(x) = |x|$ if we shift it upward by 3 units?
2. How would you shift the graph of $f(x) = |x|$ horizontally, say to the right by 2 units?
3. What would happen to the graph of $f(x) = |x|$ if we stretched it vertically by a factor of 2?
4. How do you describe the transformation of the graph of $f(x) = |x|$ if we reflect it over the x-axis?
5. How would you combine horizontal and vertical shifts to move the graph of $f(x) = |x|$ to the point (2, -3)?

Tip: To shift a graph vertically, you add or subtract a constant to/from the function, depending on the direction of the shift (positive for upward, negative for downward).