The RationalFunctionPlot(f) command plots a rational function.  If f has any asymptotes, they are also displayed.

The optional parameters opts specify the desired options for the resulting plot.  The available options are:

functionoptions = list

Specifies the plot options for f.

showslantasymptotes = true/false

Specifies whether or not to show the slant asymptotes of f.

showverticalasymptotes = true/false

Specifies whether or not to show the vertical asymptotes of f.

showremovables = true/false

Specifies whether or not to show the removable discontinuities of f.

slantasymptoteoptions = list

Specifies the plot options for the slant asymptotes (including horizontal) of f.

verticalasymptoteoptions = list

Specifies the plot options for the vertical asymptotes for f.

removableoptions = list

Specifies the plot options for the removable discontinuities for f.

caption = anything

A caption for the plot.

The default caption is constructed from the parameters and the command options. caption = "" disables the default caption. For more information about specifying a caption, see plot/typesetting.

For information on including additional plot option(s), see the plot help page.

For information on how to change the default colors, see the Student [SetColors] help page.

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

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

$\mathrm{RationalFunctionPlot}\left(\frac{1}{x^2}\,'\mathrm{verticalasymptoteoptions}'=\left['\mathrm{color}'=\mathrm{red}\right]\,'\mathrm{functionoptions}'=\left['\mathrm{color}'=\mathrm{blue}\right]\right)$

$\mathrm{RationalFunctionPlot}\left(\frac{x^2-2x-3}{x^2-1}\,\mathrm{view}=\left[-2..5\,-10..10\right]\,\mathrm{functionoptions}=\left[\mathrm{color}=\mathrm{violet}\,\mathrm{thickness}=2\right]\,\mathrm{showslantasymptotes}\,\mathrm{slantasymptoteoptions}=\left[\mathrm{color}=\mathrm{magenta}\,\mathrm{linestyle}=\mathrm{dashdot}\,\mathrm{thickness}=2\right]\,\mathrm{verticalasymptoteoptions}=\left[\mathrm{color}=\mathrm{blue}\,\mathrm{linestyle}=\mathrm{dash}\,\mathrm{thickness}=2\right]\,\mathrm{removableoptions}=\left[\mathrm{symbol}=\mathrm{soliddiamond}\,\mathrm{symbolsize}=20\,\mathrm{color}=\mathrm{green}\right]\right)$