Determine Whether the Graph of the Rational Function Has a Horizontal

question 21

Multiple Choice

Determine whether the graph of the rational function has a horizontal asymptote, an oblique asymptote, or neither. Give
the equation of the asymptote if it exists.
- $f ( x ) = \frac { 10 x ^ { 3 } - 17 x ^ { 2 } + 3 x - 1 } { 4 x ^ { 2 } - 1 }$

• A) \(\text { Oblique asymptote: } y = \frac { 5 } { 2 } x - \frac { 17 } { 4 }\)
• B) \(\text { Horizontal asymptote: } y = \frac { 5 } { 2 }\)
• C)Neither

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Definitions:

AntiAromatic

Refers to a cyclic, conjugated compound with an odd number of pairs of pi electrons that does not follow Huckel's rule, often making it less stable.

π Network

A system of connected π bonds, allowing delocalized electron movement across molecule segments.

Sulfur Atom

A chemical element with the atomic number 16, known for its yellow color and presence in many essential biochemicals and minerals.

Cyclopentadienyl Cation

A highly reactive, positively charged intermediate featuring a five-membered ring with two double bonds.