# Is x^2 - y^2 = 7  a function?

Jul 8, 2015

${x}^{2} - {y}^{2} = 7$ is not a function

#### Explanation:

${x}^{2} - {y}^{2} = 7$
could be rearranged as
$\textcolor{w h i t e}{\text{XXXX}}$${y}^{2} = {x}^{2} - 7$

So
$\textcolor{w h i t e}{\text{XXXX}}$$y = \pm \sqrt{{x}^{2} - 7}$

That is for ${x}^{2} > 7$ there is more than one value for $y$
which is contrary to the requirement for an equation to be a function.