1. The problem asks how the graph of $$g(x) = -|x - 5|$$ relates to the graph of $$f(x) = |x|$$. 2. The base function is $$f(x) = |x|$$, which is a V-shaped graph with vertex at the origin $$(0,0)$$. 3. The function $$g(x) = -|x - 5|$$ involves two transformations: - Horizontal shift right by 5 units (due to $$x - 5$$ inside the absolute value). - Reflection across the x-axis (due to the negative sign in front). 4. The vertex of $$g(x)$$ is at $$(5,0)$$ because the inside of the absolute value is zero at $$x=5$$. 5. The graph of $$g(x)$$ is a downward V-shape, shifted right 5 units from $$f(x)$$ and reflected over the x-axis. 6. This matches option B, which shows the vertex at $$(5,0)$$ and the graph opening downward. Final answer: The graph of $$g(x) = -|x - 5|$$ is the graph of $$f(x) = |x|$$ shifted 5 units to the right and reflected across the x-axis, matching option B.