Identify the Asymptotes $$f ( x ) = \frac { x ^ { 3 } - 4 x ^ { 2 } - 9 x + 8 } { x ^ { 2 } - 6 }$$

question 85

Multiple Choice

Identify the asymptotes.
- $$f ( x ) = \frac { x ^ { 3 } - 4 x ^ { 2 } - 9 x + 8 } { x ^ { 2 } - 6 }$$

• A) Vertical asymptotes: \(x = \sqrt { 6 }\) and \(x = - \sqrt { 6 }\)
• Slant asymptote: \(y = x - 4\)
• B) Vertical asymptotes: \(x = \sqrt { 6 }\) and \(x = - \sqrt { 6 }\)
• Slant asymptote: \(y = - 3 x - 16\)
• C) Vertical asymptotes: \(x = \sqrt { 6 }\) and \(x = - \sqrt { 6 }\)
• Horizontal asymptote: \(y = 1\)
• D) Vertical asymptotes: \(x = 6\) and \(x = - 6\)
• Horizontal asymptote: \(y = 1\)

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Definitions:

Spreading Activation

A cognitive process where activating one concept in the memory network triggers the activation of related concepts, facilitating information retrieval.

Shortcut

A quicker or more direct route or method than the one usually taken.

Judgment Strategies

The cognitive processes and methods individuals use to make decisions or form evaluations about different aspects of their environment.

Heuristics

Mental shortcuts or rules of thumb that simplify decision-making processes, often leading to quick but sometimes inaccurate conclusions.