The original function given is $f(x) = |x|$, which is the absolute value function. The graph shows a transformation of this function. Let's analyze the transformation step by step.

1. Reflection: The graph is reflected over the x-axis compared to $f(x) = |x|$, which means a vertical reflection. This indicates a negative sign in front of the function, making it $-|x|$.

2. Vertical Shift: The graph is shifted downward by 3 units. This indicates a vertical shift, adding $-3$ to the function.

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

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

Would you like further details or have any questions?

Here are 5 related questions for further practice:

1. What happens if we reflect the function $|x|$ over the y-axis instead of the x-axis?
2. How would the graph change if the function was $g(x) = 2|x| - 3$?
3. How can you describe a horizontal shift for the function $f(x) = |x|$?
4. What is the vertex of the function $g(x) = -|x| - 3$?
5. How does adding or subtracting a constant outside the absolute value affect the graph?

Tip: Reflections over the x-axis involve multiplying the entire function by $-1$, while reflections over the y-axis involve changing the sign inside the function.