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 $(0,0)$ 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, flipping it upside down. 4. Therefore, the vertex of $g(x)$ is at $(5,0)$, and the graph opens downward. 5. This matches option B: The graph of $g(x)$ is the graph of $f(x)$ shifted to the right 5 units and reflected in the x-axis. 6. To sketch the graph: - Start with the V-shape of $f(x) = |x|$. - Shift it right 5 units to vertex $(5,0)$. - Reflect it across the x-axis to open downward. Final answer: Option B. $$g(x) = -|x - 5|$$ This is the graph of $f(x) = |x|$ shifted right 5 units and reflected across the x-axis.