1. The problem asks to find the equation of a function $h(x)$ that first reflects the graph of $f(x) = |x|$ over the y-axis, then shifts it down 3 units. 2. Reflection over the y-axis means replacing $x$ by $-x$ in the function. So reflecting $f(x) = |x|$ over the y-axis gives: $$f(-x) = |-x|$$ Since $|-x| = |x|$, the graph remains the same after reflection. 3. Next, shifting the graph down 3 units means subtracting 3 from the function: $$h(x) = f(-x) - 3 = |x| - 3$$ 4. Therefore, the equation of the function $h(x)$ after reflecting over the y-axis and shifting down 3 units is: $$h(x) = |x| - 3$$ 5. This means the graph is still V-shaped, symmetric about the y-axis, but the vertex is now at $(0, -3)$ instead of $(0, 0)$. Final answer: $$h(x) = |x| - 3$$