Example 1: Asymptotes  Command

>	w := x -> (2*x^5+3*x^3-2*x-2)/(x^4-1);

>	Pw := plot( w(x), x=-10..10,             y=-20..20, discont=true ):

>

Pw;

>	asym := Asymptotes( w(x), x );

>	Pa1 := implicitplot( asym[1], x=-10..10,                  y=-20..20, linestyle=2 ):

>	Pa2 := implicitplot( {asym[2],asym[3]},         x=-10..10, y=-20..20, linestyle=3 ):

>	display( [ Pw, Pa1, Pa2 ] );

>

Example 2: Horizontal Asymptotes

>	g := x -> (x^4-2*x^3+2*x-1)/(x^4+1);

>	Pg := plot( g(x), x=-20..20 ):

>

Pg;

>	q1 := limit( g(x), x=infinity );

>	q2 := limit( g(x), x=-infinity );

>	horiz := { q1, q2 };

>	Ph := plot( horiz, x=-20..20, color=cyan ):

>	display( [ Pg, Ph ] );

>

Example 3: Vertical Asymptotes

>	f := x -> (sin(x)-cos(x)+1)/(x^3-3*x+2);

>	Pf := plot( f(x), x=-4..4,             y=-10..10, discont=true ):

>

Pf;

>	q1 := denom( f(x) );

>	q2 := solve( q1=0, {x} );

>	vert := { x=-2, x=1 };

>	Pv := implicitplot( vert, x=-2*Pi..2*Pi,                     y=-20..20, color=blue ):

>	display( [ Pf, Pv ] );

>

Example 4: Oblique Asymptotes (for Rational Functions)

>	u := x -> (3*x^3-4*x^2-5*x+3)/(x^2+1);

>	Pu := plot( u(x), x=-10..10 ):

>

Pu;

>	q1 := numer( u(x) );

>	q2 := denom( u(x) );

>	q3 := quo( q1, q2, x );

>	q4 := rem( q1, q2, x );

>	u2 := q3 + q4/q2;

>	u(x) = simplify( u2 );

>	Po := plot( q3, x=-10..10, color=pink ):

>	display( [ Pu, Po ] );

>