Graphs Approaching Asymptotes 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?
 A: To summarize what the commenters said, you can always subtract either the $x$-value or the value of the function to find the distance.
In other words, if you have some function $f(x)$ that has a horizontal asymptote at $y=a$ and/or a vertical asymptote at $x=b$, the distance of the function from the horizontal asymptote will always be $|a-f(x)|$, and the distance of the function from the vertical asymptote will always be $|b-x|$.

If we want to make things more interesting and talk about oblique asymptotes, the problem gets much more complicated, since the distances we'll now be concerned with will no longer be perfectly vertical or horizontal. They will, however, be orthogonal to the oblique asymptote, which is the principle off of which I based this Desmos page.
It involves formulas that are probably too long to fit on a single line here, but I did find a way to find the distance between a general rational function of the form $$f(x)=\frac{a^2+bx+c}{dx+h}$$ (using $h$ there to avoid confusion with the base of the natural logarithm and the functions I named $f(x)$ and $g(x)$ in Desmos) and its oblique asymptote.
