QuestionSolve $x^{2}+y^{2}=81$ for $y$. Find the positive and negative functions: $y_{1}=\square$, $y_{2}=\square$.

Studdy Solution
Now we can write down the two explicit functions. The positive square root gives us the first function, $y_{1}$, and the negative square root gives us the second function, $y_{2}$.
$$y_{1} = \sqrt{81 - x^{2}}$$$$y_{2} = -\sqrt{81 - x^{2}}$$So, the two explicit functions are $y_{1} = \sqrt{81 - x^{2}}$ and $y_{2} = -\sqrt{81 - x^{2}}$.