1. **State the problem:** Determine if the given rule defines $y$ as a function of $x$ based on the pairs: $$\begin{array}{c|c} x & y \\ \hline -81 & 9 \\ -16 & 4 \\ -1 & 1 \\ 0 & 0 \\ -1 & -1 \\ -16 & -4 \\ -81 & -9 \\ \end{array}$$ 2. **Recall the definition of a function:** A relation defines $y$ as a function of $x$ if and only if each $x$-value corresponds to exactly one $y$-value. 3. **Analyze the given pairs:** - The $x$-value $-1$ corresponds to $y=1$ and also $y=-1$. - The $x$-value $-16$ corresponds to $y=4$ and also $y=-4$. - The $x$-value $-81$ corresponds to $y=9$ and also $y=-9$. 4. **Conclusion:** Since some $x$-values correspond to more than one $y$-value, $y$ is **not** a function of $x$. **Final answer:** **D. No, because at least one $x$-value of the given rule corresponds to more than one $y$-value.**