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

1 Answer
Truong-Son N.
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)#

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