The Asymptotes(f(x), x) calling sequence returns all the vertical, horizontal, and diagonal asymptotes of the expression f(x) as a list of equations of the form $x=\mathrm{value}$, $y=\mathrm{value}$, and $y=\mathrm{value}x$, respectively.

The Asymptotes(f(x), x = a..b) calling sequence returns all the vertical asymptotes in the interval [a, b], and horizontal and diagonal asymptotes of the expression f(x) as a list of equations of the form $x=\mathrm{value}$, $y=\mathrm{value}$, and $y=\mathrm{value}x+\mathrm{value}$, respectively.

The default name of the dependent variable is y unless y is specified as the independent variable.

If the independent variable can be uniquely determined from the expression, the parameter x need not be included in the calling sequence.

If the expression has an infinite number of vertical asymptotes, a warning message and sample vertical asymptotes are returned.

The opts argument can contain the following equation that sets computation options.

numeric = true or false

Whether to use numeric methods (using floating-point computations) to find the asymptotes of the expression. If this option is set to true, the points a and b must be finite and are set to $\mathrm{-10}$ and $10$ if they are not provided. By default, the value is false.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{Calculus1}\right]\right)\:$

$\mathrm{Asymptotes}\left(\frac{1}{x-3}+2x\,x\right)$

$\left[y=2x\,x=3\right]$

$\mathrm{Asymptotes}\left(\frac{1}{x-3}+2x\,x=0..2\right)$

$\left[y=2x\right]$

$\mathrm{Asymptotes}\left(\tan \left(x\right)\,0..10\right)$

$\left[x=\frac{\mathrm{\pi }}{2}\,x=\frac{3\mathrm{\pi }}{2}\,x=\frac{5\mathrm{\pi }}{2}\right]$

$\mathrm{Asymptotes}\left(\tan \left(x\right)\,0..10\,\mathrm{numeric}\right)$

$\left[x=1.570796327\,x=4.712388981\,x=7.853981635\right]$

$\mathrm{Asymptotes}\left(\frac{x^3-2x^2+x}{x^3-3x^2-x+3}\,x\right)$

$\left[y=1\,x=\mathrm{-1}\,x=3\right]$