I've been wondering this for a while. For graphs that approach asymptotes, are there certain formulas that can determine the distance between the graph and the asymptote as $x$ gets infinitely small or large?

  • $\begingroup$ For horizontal and vertical asymptotes, just "subtract" the equations: So if you have $f(x) = \frac{1}{x-2}$, then you have a vertical asymptote at $x=2$. So the distance function would be $| 2 - x|$ (if you want to find the distance from the asymptote for some input $x$) $\endgroup$ – user90667 May 14 '15 at 5:15
  • $\begingroup$ For the vertical asymptote, don't you mean the distance is $|2-x_0|$ instead of $|2-f(x_0)|$? $\endgroup$ – Jason Chen May 14 '15 at 5:17
  • $\begingroup$ I edited my comment; now it should be correct. $\endgroup$ – user90667 May 14 '15 at 5:18
  • $\begingroup$ That's the same as $x_0$. I don't see why adding the extra functions helps explain it better. $\endgroup$ – Jason Chen May 14 '15 at 5:20

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