Find the oblique asymptote, if any, of the rational function.
-$$f ( x ) = \frac { x ^ { 3 } - 5 x ^ { 2 } + 4 x - 1 } { x ^ { 2 } + 4 x }$$
A) $y = x - 9$
B) $y = x + 9$
C) None
D) $y = x$

Question

Quizplus · Accepted Answer

To find the oblique asymptote of the given rational function, we divide the numerator by the denominator. The division $ \frac { x ^ { 3 } - 5 x ^ { 2 } + 4 x - 1 } { x ^ { 2 } + 4 x }$ results in $x - 9$ with a remainder, indicating that $y = x - 9$ is the oblique asymptote.

Find the Oblique Asymptote, If Any, of the Rational Function f(x)=x3−5x2+4x−1x2+4xf ( x ) = \frac { x ^ { 3 } - 5 x ^ { 2 } + 4 x - 1 } { x ^ { 2 } + 4 x }f(x)=x2+4xx3−5x2+4x−1​

Find the Oblique Asymptote, If Any, of the Rational Function $f ( x ) = \frac { x ^ { 3 } - 5 x ^ { 2 } + 4 x - 1 } { x ^ { 2 } + 4 x }$