Question 910848
4x^3-9x^2-9x-6 /( -6x^2-6x+5 )
Using Long Division to determine non- verticle asymptote
-2x/3 + 11/6 +  (44x-101)/6/(-6x^2-6x+5)
......
As x gets very large...(44x-101)/6/(-6x^2-6x+5)approaches 0
....
y = (-2/3)x + 11/6 (Green) is the oblique non-verticle asymptote
 Does f(x) intersect its non-verticle asymptote? No 

{{{drawing(300,300,   -10,10,-10,10,  
 grid(1),

graph( 300, 300, -10,10,-10,10,0,(-2/3)x + 11/6, (4x^3-9x^2-9x-6) / (-6x^2-6x+5) ))}}}