>	with(plots):

Warning, the name changecoords has been redefined

>	f:=(x^4+x^3-7*x^2-x+6)/(x^2-16);

>	fprime:=diff(f,x);

>	Q:=quo(x^4+x^3-7*x^2-x+6,x^2-16,x);

>	fGraph:=plot(f,x=-10..10,y=-100..100,thickness=2,discont=true):

>	Qgraph:=plot(x^2+x+9,x=-10..10,y=-100..100,thickness=2,color=blue):

>	VertAsym1:=implicitplot(x=-4,x=-10..10,y=-100..100,thickness=2,color=blue):

>	VertAsym2:=implicitplot(x=4,x=-10..10,y=-100..100,thickness=2,color=blue):

The function is graphed below in red along with the vertical asymptotes in blue and the "asymptotic parabola" in blue.

>	display(fGraph,Qgraph,VertAsym1,VertAsym2);

>	display(fGraph);

Notice that if we do not set "discont=true" Maple attempts to connect points on each side of a vertical asymptote.  The result is to draw nearly vertical lines that appear to be part

of the graph of the function.

>	fGraph2:=plot(f,x=-10..10,y=-100..100,thickness=2):

>	display(fGraph2);

>	fsolve({fprime},{x},-6..-4);

>	eval(f,x=-5.088511437);

>	fsolve({fprime},{x},-4..-2);

>	eval(f,x=-2.412333637);

>	fsolve({fprime},{x},-1..1);

>	eval(f,x=-.7436981272e-1);

>	fsolve({fprime},{x},1..2);

>	eval(f,x=1.600749930);

>	fsolve({fprime},{x},4..6);

>	eval(f,x=5.474464957);

Let's look at a "blow-up" of the graph around some of the critical points.

>	plot(f,x=-3..3,y=-3..3,thickness=2);

>