1. The problem asks to sketch the graph of the transformed function $$-f(x)-1$$ given the original graph of $$f(x)$$. 2. The original graph is a V-shaped graph centered at the origin with vertex at (0,0). The left arm goes downward from (0,0) to (-2,2) and the right arm goes upward from (0,0) to (2,2). 3. The transformation $$-f(x)$$ reflects the graph of $$f(x)$$ across the x-axis. This means every y-value of $$f(x)$$ is multiplied by -1. 4. Applying $$-f(x)$$ to the vertex at (0,0) keeps it at (0,0) because $$-0=0$$. 5. The left arm endpoint at (-2,2) becomes (-2,-2) after reflection. 6. The right arm endpoint at (2,2) becomes (2,-2) after reflection. 7. Next, subtracting 1 from $$-f(x)$$ shifts the entire graph down by 1 unit. 8. The vertex moves from (0,0) to (0,-1). 9. The left arm endpoint moves from (-2,-2) to (-2,-3). 10. The right arm endpoint moves from (2,-2) to (2,-3). 11. The transformed graph is a V-shaped graph with vertex at (0,-1), left arm from (0,-1) to (-2,-3), and right arm from (0,-1) to (2,-3). Final answer: The graph of $$-f(x)-1$$ is the reflection of $$f(x)$$ across the x-axis followed by a downward shift of 1 unit, resulting in a V-shaped graph with vertex at (0,-1) and arms extending to (-2,-3) and (2,-3).