1. **State the problem:** We are given two functions: the original cubic function $f(x) = x^3$ and a transformed function $h(x) = -(x + 2)^3 - 4$. We want to understand the transformations applied to $f(x)$ to get $h(x)$. 2. **Recall the base function and transformations:** The base function is $f(x) = x^3$, a cubic curve centered at the origin. 3. **Analyze the transformations in $h(x)$:** - The term $(x + 2)$ inside the cube indicates a horizontal shift. Specifically, $x$ is replaced by $x + 2$, which shifts the graph 2 units to the left. - The negative sign in front of the cube, $-(x + 2)^3$, reflects the graph across the x-axis. - The $-4$ outside the cube shifts the graph 4 units downward. 4. **Summary of transformations:** - Shift left by 2 units - Reflect across the x-axis - Shift down by 4 units 5. **Final transformed function:** $$h(x) = -(x + 2)^3 - 4$$ This fully describes the transformation from $f(x)$ to $h(x)$.