topsquark
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- Aug 27, 2012
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reference: https://www.freemathhelp.com/forum/...or-give-a-counter-example.118955/#post-472024
-Dan
I feel like we're being unnecessarily picky here. There is no subset of the real numbers where the vertical line test actually fails in this example. A function is still a function on the real numbers even if there are subsets of real numbers that the function cannot be evaluated at. For example, f(x) = 1/x is considered to be a function on the set of real numbers, even if it cannot be evaluated at x = 0. Right? At least I've never run into anyone who has said that 1/x is not a function over the reals.\(\displaystyle y=-\sqrt{x}\) is not a function on the set of real numbers.
-Dan