Use Limits to Describe the Behavior of the Rational Function $$f ( x ) = \frac { 1 } { x ^ { 2 } - 9 }$$

question 72

Multiple Choice

Use limits to describe the behavior of the rational function near the indicated asymptote.
- $$f ( x ) = \frac { 1 } { x ^ { 2 } - 9 }$$
Describe the behavior of the function near its vertical asymptotes.

• A) \(\lim _ { x \rightarrow 3 ^ { - } } f ( x ) = - \infty , \lim _ { x \rightarrow 3 ^ { + } } f ( x ) = 0 , \lim _ { x \rightarrow 3 ^ { - } } f ( x ) = - \infty , \lim _ { x \rightarrow 3 ^ { + } } f ( x ) = \infty\)
• B) \(\lim _ { x \rightarrow 3 ^ { - } } f ( x ) = 0 , \lim _ { x \rightarrow 3 ^ { + } } f ( x ) = - \infty , \lim _ { x - 8 ^ { - } } f ( x ) = - \infty , \quad \lim _ { x \rightarrow 8 ^ { + } } f ( x ) = 0\)
• C) \(\lim _ { x \rightarrow 3 ^ { - } } f ( x ) = \infty , \lim _ { x \rightarrow 3 ^ { + } } f ( x ) = - \infty , \lim _ { x \rightarrow 8 ^ { - } } f ( x ) = \infty , \lim _ { x \rightarrow 8 ^ { + } } f ( x ) = - \infty\)
• D) \(\lim _ { x \rightarrow 3 ^ { - } } f ( x ) = x , \lim _ { x \rightarrow 3 ^ { + } } f ( x ) = - \infty , \lim _ { x \rightarrow 3 ^ { - } } f ( x ) = - \infty , \quad \lim _ { x \rightarrow 3 ^ { + } } f ( x ) = x\)

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