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

1 Answer
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 - 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)