Question

he notion of an asymptote can be extended to include curves as well as lines. Specifically, we say that curves y=f(x) and y=g(x) are asymptotic as ∞x→+∞ provided

∞limx→+∞[f(x)-g(x)]=0
and are asymptotic as ∞x→-∞ provided

∞limx→-∞[f(x)-g(x)]=0.

Determine a simpler function g(x) such that y=f(x)=-x3+2x2+2x-3/x-2 is asymptotic to y=g(x) as ∞x→+∞ or ∞x→-∞. Use a graphing utility to generate the graphs of y=f(x) and y=g(x) and identify the vertical asymptote.

Answer 1