(02-18-2015, 12:23 AM)Error Wrote: Edit: I think I misunderstood that, so here's a quick note regarding the case of 1/x: the function will never cross the y-axis and will thus not "flip" signs as it approaches infinity, as 1/0 is not defined as stated earlier.
It's rather a consensus than an observation that the graph of the 1/x function never crosses any of the axes. But theoretically it could, in the infinity (not when just approaching it), where then it flips signs and continues going back towards zero. Imagine linear functions actually being 3D circles with infinite radius. For them you'd need two points where values flip signs, one is zero, the other can be infinity.
(More mindfech: x/0=inf. and x/inf.=0 could be easily possible and show how similar they are, even tho the current mathematical consensus is that x/0=undefined and only lim(y->0)x/y=inf., same going for the x/inf. values.)