305 MrG More Rational Functions!

2468 days ago by MATH4R2013

#1) f(x)=(x^2+x-12)/(x^2-x-6) #1) prove that the horizontal asymptote is y=1 by long division. f(x)=(x^2+x-12)/(x^2-x-6) show(f(x)) show(f(x).partial_fraction()) 
       

#2) f(x)=(x^2+x-12)/(x^2-x-6) #2) why does f(x) only have 1 vertical asymptote? show(factor(x^2+x-12)) show(factor(x^2-x-6)) show(factor((x^2+x-12)/(x^2-x-6))) 
       


#3) f(x)=(x^2+x-12)/(x^2-x-6) #3) show that the intercepts of f(x) are (-4,0) and (0,2). show(solve(f(x)==0,x)) show(f(0)) 
       

#4) f(x)=(x^2+x-12)/(x^2-x-6) #4) make a complete sketch of f(x) labeling all intercepts and asymptotes. p1=plot(f(x),-10,-2,color='red') p2=plot(f(x),-2,3,color='green') p3=plot(f(x),3,10,color='purple') p4=plot(1,-10,10) (p1+p2+p3+p4).show(ymin=-5,ymax=5) 
       
#5) f(x)=(x^2+x-12)/(x^2-x-6) #5) state the domain and range of f(x). #5) domain: (-inf,-2)U(-2,3)U(3,+inf) #5) range: (-inf,1)U(1,+inf) 
       
#6) f(x)=(x^2+x-12)/(x^2-x-6) #6) discuss the important limits show(limit(f(x),x=-infinity)) show(limit(f(x),x=-2,dir='left')) show(limit(f(x),x=-2,dir='right')) show(limit(f(x),x=3,dir='left')) show(limit(f(x),x=3,dir='right')) show(limit(f(x),x=infinity))