Question

f(x)=x^3-3x^2-3x-8/(-3x^2-4x-6)
Find the equation of the non-vertical asymptote.
What is the smallest value of x at which f(x) intersects its non-vertical asymptote?

the non vertical asymptote is -1/3x + 13/9 i found that using synthetic division and i know there is an intersect its non-vertical asymptote but i don't know how to find it....

Answer 1

I agree on the asymptote.

So set the intercepts equal..

-x/3+ 13/9= (x^3-3x^2-3x-8)/(-3x^2-4x-6)

+x^3 +4x^2/3+2x-13/3 x^2 -52/9x-26/3=x^3-3x^2-3x-8

combining terms
x^2 (4/3-13/3+3) +x(2+3 -52/9)-26/3+8=0

check that several times. then use the quadratic equation to solve for x