1. The problem asks how the graph of $g(x) = -|x - 5|$ is related to the graph of $f(x) = |x|$. 2. Recall the graph of $f(x) = |x|$ is a V-shaped graph with vertex at the origin $(0,0)$, opening upward. 3. The function $g(x) = -|x - 5|$ involves two transformations: - Inside the absolute value, $x - 5$ shifts the graph of $|x|$ to the right by 5 units. - The negative sign outside the absolute value reflects the graph across the x-axis (flips it upside down). 4. Therefore, the graph of $g(x)$ is the graph of $f(x)$ shifted right 5 units and reflected in the x-axis. 5. This matches option C. 6. To sketch $g(x)$, start with the vertex of $f(x)$ at $(0,0)$, shift it right to $(5,0)$, then flip the V shape downward. Final answer: C. The graph of $g(x)$ is the graph of $f(x)$ shifted to the right 5 units and reflected in the x-axis.