1. The problem asks how the graph of $g(x) = -|x - 5|$ relates to the graph of $f(x) = |x|$ and to sketch the graph of $g(x)$. 2. Recall the base function $f(x) = |x|$ is a V-shaped graph with vertex at $(0,0)$ opening upward. 3. The function $g(x) = -|x - 5|$ involves two transformations: - Horizontal shift: $x - 5$ shifts the graph of $|x|$ to the right by 5 units. - Reflection: The negative sign in front of the absolute value reflects the graph across the x-axis, flipping it upside down. 4. Therefore, the vertex of $g(x)$ is at $(5,0)$, and the graph opens downward. 5. The graph of $g(x)$ is the graph of $f(x)$ shifted right 5 units and reflected in the x-axis. 6. The correct description is: The graph of $g(x)$ is the graph of $f(x)$ shifted right 5 units and reflected in the x-axis. 7. Among the options, the graph at the top-right position matches this description: an inverted V-shaped graph opening downward with vertex at approximately $(5,0)$. Final answer: The graph of $g(x) = -|x - 5|$ is the graph of $f(x) = |x|$ shifted right 5 units and reflected across the x-axis. $$g(x) = -|x - 5|$$ This matches option B (top-right graph).