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

question 485

Multiple Choice

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) \(\lim _ { x - \theta ^ { - } } f ( x ) = \infty , \quad \lim _ { x - \theta ^ { + } } f ( x ) = \infty\)

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Definitions:

Confidence Interval

An estimate expressed as a range that likely contains a population parameter, characterized by a lower and upper bound computed from sample data.

Two Population Means

A statistical comparison between the mean values of two distinct groups or populations.

Sample Means

The arithmetic averages derived from multiple subsets of a population, reflecting the central tendency of each subset.

Population Means

The mean values calculated from the entirety of specified populations.