304 MrG What's a Rational Function?

2477 days ago by MATH4R2013

#1) #given rational function f(x)=x^3/(x^4-1) show(f(x)) #find x-intercepts show(solve(x^3==0,x)) #when is f(x) undefined? show(factor(f(x))) show(solve(x^4-1==0,x)) #find y-intercept show(f(0)) #graph f(x) p1=plot(f(x)) p2=plot(f(x),-2,-1) p3=plot(f(x),1,2) show(p1+p2+p3) #discuss end behavior show(lim(f(x),x=infinity)) show(lim(f(x),x=-infinity)) #discuss local behavior show(lim(f(x),x=1,dir='left')) show(lim(f(x),x=1,dir='right')) 
       









#2) #given rational function f(x)=(-3*x^2+2)/(x-1) show(f(x)) #find the x-intercepts show(solve(-3*x^2+2==0,x)) #when is f(x) undefined? show(solve(x-1==0,x)) #find the y-intercept show(f(0)) #graph f(x) and the slant asymptote p1=plot(f(x),-10,1) p2=plot(f(x),1,10) p3=plot(-3*x-3,-10,10) show(p1+p2+p3) #discuss end behavior show(lim(f(x),x=infinity)) show(lim(f(x),x=-infinity)) #describe f(x) near the vertical asymptote show(lim(f(x),x=1,dir='left')) show(lim(f(x),x=1,dir='right'))