SOLUTION: Find the parabolic asymptote of the function. y = {{{(6x^3 - 4x^2 - x + 4)/(3x - 5)}}}

Algebra ->  Rational-functions -> SOLUTION: Find the parabolic asymptote of the function. y = {{{(6x^3 - 4x^2 - x + 4)/(3x - 5)}}}      Log On


   

Question 860505: Find the parabolic asymptote of the function.
y = %286x%5E3+-+4x%5E2+-+x+%2B+4%29%2F%283x+-+5%29
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
Q:
Find the parabolic asymptote of the function.
y = %286x%5E3+-+4x%5E2+-+x+%2B+4%29%2F%283x+-+5%29
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A:
First we divide the numerator by the denominator.

The result is 2x%5E2+%2B+2x+%2B+3+%2B+19%2F%283x+-+5%29.
The fractional part 19%2F%283x+-+5%29 approaches zero as x decreases without bound. Therefore, the parabolic asymptote is highlight%28y+=+2x%5E2+%2B+2x+%2B+3%29.
Here's the graph: