# How do you use the vertical line test to show x^2+y^2=25 is a function?

Jun 4, 2015

The problem is that ${x}^{2} + {y}^{2} = 25$ is not a function.

Using the vertical line test with the vertical line
$\textcolor{w h i t e}{\text{XXXX}}$$x = 0$
we see that
$\textcolor{w h i t e}{\text{XXXX}}$there are two solutions for $y$ ($+ 5$ and $\left(- 5\right)$)

That is there are two solution points on the vertical line $x = 0$
and therefore
${x}^{2} + {y}^{2} = 25$ is not a function.