# How do you use the vertical line test to show x^2-4y^2+4=0 is a function?

Jun 15, 2015

It's self-explanatory; draw a vertical line and see if it intersects more than once with the curve. If so, it's not a single-valued function and therefore it's not a single function.

${x}^{2} - 4 {y}^{2} + 4 = 0$

${x}^{2} + 4 = 4 {y}^{2}$

$y = \pm \sqrt{\frac{{x}^{2} + 4}{4}}$

And evidently, this is not one function, but two. You have a $+$ and $-$ equation. Even the inverse isn't a single function.

${y}^{2} - 4 {x}^{2} + 4 = 0$

${y}^{2} = 4 {x}^{2} - 4$

$y = \pm \sqrt{4 {x}^{2} - 4} = \pm 2 \sqrt{{x}^{2} - 1}$