112.sagews

f(x)=(8*x^2-6*x+6)/(2*x-2); f(x)

(8*x^2 - 6*x + 6)/(2*x - 2)

asymptotesverticales=solve( 2*x-2,x); asymptotesverticales

[x == 1]

limit(f(x),x=1, dir="plus")

+Infinity

limit( f(x), x=1, dir="minus")

-Infinity

a1=limit(f(x)/x,x=-infinity);a1

4

b1=limit(f(x)-a1*x,x=infinity);b1

1

asymptote1(x)=a1*x+b1;asymptote1(x)

4*x + 1

a2=limit(f(x)/x,x=-infinity);a2

4

b2=limit(f(x)-a1*x,x=-infinity);b2

1

asymptote2(x)=a2*x+b2;asymptote2(x)

4*x + 1

P1=plot(f(x),(x,-5,5))

P2=plot(asymptote1(x),(x,-5,5),rgbcolor=(1,0,0))

P3=plot(asymptote2(x),(x,-5,5),rgbcolor=(1,0,0))

oishow(P1+P2+P3,ymin=-20,ymax=20)