# Is x^2+y^2=9 a function?

Aug 1, 2015

${x}^{2} + {y}^{2} = 9$ is not a function

#### Explanation:

In order for an equation to represent a function any single value of $x$ must have at most one corresponding value of $y$ which satisfies the equation.

For ${x}^{2} + {y}^{2} = 9$
$\textcolor{w h i t e}{\text{XXXX}}$if (for example) $x = 0$
$\textcolor{w h i t e}{\text{XXXX}}$there are two values for $y$ (namely $+ 3$ and $- 3$) which satisfy the equation

and therefore the equation is not a function.