Use limits to describe the behavior of the rational function near the indicated asymptote.
-$$f ( x ) = \frac { x + 1 } { x ^ { 2 } - 2 x }$$
Describe the behavior of the function near its horizontal asymptote (the end behavior).
A) $\lim _ { x \rightarrow \infty } f ( x ) = - \infty , \quad \lim _ { x \rightarrow } f ( x ) = \infty$
B) $\lim _ { x \rightarrow \infty } f ( x ) = - 1 , \lim _ { x \rightarrow \infty } f ( x ) = 1$
C) $\lim _ { x \rightarrow \infty } f ( x ) = 0 , \lim _ { x \rightarrow \infty } f ( x ) = 0$
D) $\lim _ { x - \theta ^ { - } } f ( x ) = \infty , \quad \lim _ { x - \theta ^ { + } } f ( x ) = \infty$

Question

Quizplus · Accepted Answer

For the given function $f(x) = \frac{x + 1}{x^2 - 2x}$, as $x$ approaches infinity, the degree of the polynomial in the denominator is higher than that in the numerator. This means the function approaches 0 as $x$ approaches infinity or negative infinity, indicating a horizontal asymptote at $y = 0$.

Use Limits to Describe the Behavior of the Rational Function f(x)=x+1x2−2xf ( x ) = \frac { x + 1 } { x ^ { 2 } - 2 x }f(x)=x2−2xx+1​

Use Limits to Describe the Behavior of the Rational Function $f ( x ) = \frac { x + 1 } { x ^ { 2 } - 2 x }$