Oblique Asymptote

Author

Eric W. Weisstein
September 1, 2026

This notebook downloaded from https://mathworld.wolfram.com/notebooks/PlaneCurves/ObliqueAsymptote.nb.

For more information, see Eric's MathWorld entry https://mathworld.wolfram.com/ObliqueAsymptote.html.

©2026 Wolfram Research, Inc. except for portions noted otherwise

Figure

The graph of y=x+1/x approaches the dashed oblique asymptote y=x as the absolute value of x increases.

Module[{asymptoteColor,curveColor,ink},curveColor=RGBColor[0.15,0.45,0.8];asymptoteColor=RGBColor[0.9,0.4,0.1];ink=LightDarkSwitched[Black,White];Plot[{x+(1/x),x},{x,-4,4},Exclusions->{0},PlotStyle->{Directive[curveColor,AbsoluteThickness[2.5]],Directive[asymptoteColor,Dashed,AbsoluteThickness[2]]},AxesStyle->ink,BaseStyle->Directive[16,FontFamily->"Times"]]]