${}$
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 connectthedots graphing algorithm, and is not the vertical asymptote. (It is removed (in the Plot Builder) by checking "discont" in the 2D 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 $\frac{P\left(x\right)}{Q\left(x\right)}\:$

Asymptotes
Horizontal

Oblique

Vertical




Plot


