Give the equation of the horizontal asymptote, if any, of the function.
-$$f ( x ) = \frac { x ( x - 1 ) } { x ^ { 3 } + 49 x }$$
A) $x = 0 , x = - 49$
B) $y = 1$
C) no horizontal asymptotes
D) $y = 0$

Question

Quizplus · Accepted Answer

Horizontal asymptotes are found by examining the behavior of a function as $x$ approaches infinity. For the given function, as $x$ approaches infinity, the highest degree terms in the numerator and denominator ($x^2$ and $x^3$, respectively) dominate, leading to the function approaching $0$. Thus, the horizontal asymptote is $y = 0$.

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