1. **State the problem:** Find the function $f(x)$ given by $$f(x) = -(x+1)^3 + 2.$$ 2. **Understand the function:** This is a cubic function shifted and reflected. 3. **Rewrite the function:** $$f(x) = -(x+1)^3 + 2$$ means take the cube of $(x+1)$, then multiply by $-1$, and finally add $2$. 4. **Evaluate at some points:** - At $x=0$: $$f(0) = -(0+1)^3 + 2 = -1 + 2 = 1$$ - At $x=-1$: $$f(-1) = -0 + 2 = 2$$ 5. **Interpretation:** The graph is a cubic curve reflected over the x-axis and shifted up by 2 units. 6. **Summary:** The function is $$f(x) = -(x+1)^3 + 2.$$ This completes the problem.