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 or negative infinity. For the given function $f(x) = \frac{x(x - 1)}{x^3 + 49x}$, we can simplify the expression by dividing the highest power of $x$ in the numerator and denominator. This simplifies to $\frac{x^2}{x^3}$ as $x$ approaches infinity, which simplifies further to $\frac{1}{x}$, indicating that the function approaches $0$ as $x$ approaches infinity or negative infinity. Therefore, the horizontal asymptote is $y = 0$.

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