Question

find any x intercepts
find any veritcal asymptote(s)
find any y intercepts
find any horizontal or oblique asymptotes
determine wherther or not the grpah cosses the horizontal or oblique asymptot. if so determine where

F(x)=6x^3+3x^2-3x over 2x^3-7x^2+7x-2

Answer 1

a 3x factors on top
3x(2x^2+x-1)=0
3x(2x-1)(x+1)=0
therefore x-intercepts at -1,0,1/2

Answer 2

okay what else?

Answer 3

same degree on top and bottom, so horizontal asymptote at y = 6/2 = 3

Answer 4

for vertical asymptotes, you have to find zeroes of the cubic function on bottom

Answer 5

x=1 is a solution, factor out a (x-1)
using synthetic division
1 | 2 -7 7 -2
2 -5 2
2 -5 2 0

2x^2 -5x +2 =0
(2x-1)(x-2) = 0

vertical asymptotes at 1/2,1,2

Answer 6

actually there is a point of discontinuity at x=1/2
the limit of f(x) at x=1/2 is 3