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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Definitions:

Quoted Loan Rates

The interest rates that lenders provide to potential borrowers when quoting the costs of a loan.

APR

Annual Percentage Rate, a measure used to compare the annual cost of borrowing or the annual yield from an investment, including interest and fees.

Quoted Loan Rates

The interest rates that banks or other lenders advertise as available to borrowers.