Give the equation of the oblique asymptote, if any, of the function.
-$$f ( x ) = \frac { 2 x ^ { 3 } + 11 x ^ { 2 } + 5 x - 1 } { x ^ { 2 } + 6 x + 5 }$$
A) $y = 0$
B) $y = 2 x - 1$
C) $y = 2 x$
D) $y = 2 x + 1$

Question

Quizplus · Accepted Answer

To find the equation of the oblique asymptote for the given function, we divide the numerator by the denominator. The quotient (ignoring the remainder) gives the equation of the oblique asymptote. For the given function, dividing $2x^3 + 11x^2 + 5x - 1$ by $x^2 + 6x + 5$ yields a quotient of $2x - 1$, which means the equation of the oblique asymptote is $y = 2x - 1$.

Give the Equation of the Oblique Asymptote, If Any, of the Function