Graph fx=xx−1, showing both its horizontal and vertical asymptotes.
A naive graph obtained from the Plot Builder, for example, will have a nearly vertical line that looks like the asymptote x = 1. However, this line is an artifact of Maple's connect-the-dots graphing algorithm, and is not the vertical asymptote. (It is removed (in the Plot Builder) by checking "discont" in the 2-D Options panel.) Note also that Maple's ordinary graphing tools will not provide the horizontal asymptote y = 1.
The most robust interactive tool for graphing a rational function and its asymptotes is found at
Tools≻Tasks≻Browse: Algebra≻Rational Function - Graph and Asymptotes
This task template accepts a rational function, and provides the equations of any of its asymptotes. There is also a button that launches the Rational Functions tutor in which the appropriate graph, with asymptotes, is drawn. When this tutor is closed, the graph is returned to the underlying task template.
Rational Function Tutor
Enter a rational function PxQx:
Use the RationalFunctionPlot command as shown to the right.
The RationalFunctionPlot command will draw the required graph, but it will not provide the equations of the asymptotes. The
tutor in the Student Precalculus package will.
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