Give the equation of the oblique asymptote, if any, of the function.
-$$f ( x ) = \frac { x ^ { 2 } + 8 x + 5 } { x + 4 }$$
A) $x = y + 4$
B) $y = x - 12$
C) $y = x + 4$
D) no oblique asymptotes

Question

Quizplus · Accepted Answer

To find the equation of the oblique asymptote for the given function, we divide the numerator by the denominator. The division $ \frac { x ^ { 2 } + 8 x + 5 } { x + 4 }$ gives a quotient of $x + 4$ with a remainder. Since the degree of the numerator is exactly one more than the degree of the denominator, there is an oblique asymptote given by the quotient, which is $y = x + 4$.

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