1. **State the problem:** Given the equation $x + 9 = 3y^2$, determine the functional relationship between $x$ and $y$. 2. **Rewrite the equation:** $$x + 9 = 3y^2$$ Solve for $x$: $$x = 3y^2 - 9$$ This shows $x$ expressed explicitly as a function of $y$. 3. **Check if $y$ is a function of $x$:** Rewrite the original equation to solve for $y$: $$3y^2 = x + 9$$ $$y^2 = \frac{x + 9}{3}$$ $$y = \pm \sqrt{\frac{x + 9}{3}}$$ 4. **Interpretation:** Since $y$ has two possible values (positive and negative square roots) for each $x$ (except when $x = -9$), $y$ is not a function of $x$ because a function must assign exactly one output for each input. 5. **Conclusion:** - $x$ is a function of $y$ because for each $y$ there is exactly one $x$. - $y$ is not a function of $x$ because for some $x$ there are two possible $y$ values. **Final answer:** $x$ is a function of $y$, but $y$ is not a function of $x$.