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

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

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Answer 1 · 2015-06-15T16:42:43

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.

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

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

$y = pmsqrt((x^2 + 4)/4)$

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

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

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

$y = pmsqrt(4x^2 - 4) = pm2sqrt(x^2 - 1)$

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

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