#### topsquark

##### Full Member

- Joined
- Aug 27, 2012

- Messages
- 580

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 functionon the set of real numbers.

-Dan