SOLUTION: Find the equation of the non-verticle asymptote. f(x)= 4x^3-9x^2-9x-6 / -6x^2-6x+5 y= ? Does f(x) intersect its non-verticle asymptote? (yes or no) What is the smallest

Question 910848: Find the equation of the non-verticle asymptote.
f(x)= 4x^3-9x^2-9x-6 / -6x^2-6x+5
y= ?
Does f(x) intersect its non-verticle asymptote? (yes or no)
What is the smallest value of x at which f(x) intersects its non-verticle asymptote? Leave blank if answered no to question above.
Thank you for your help I can't figure this one out at all.
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
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

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