Graph the Rational Function $f ( x ) = \frac { x ^ { 4 } - 3 x ^ { 3 } + x ^ { 2 } - x - 12 } { 2 x ^ { 3 } + 5 x ^ { 2 } - 28 x - 15 }$

Essay

Graph the rational function $f ( x ) = \frac { x ^ { 4 } - 3 x ^ { 3 } + x ^ { 2 } - x - 12 } { 2 x ^ { 3 } + 5 x ^ { 2 } - 28 x - 15 }$ and determine all vertical asymptotes. Then graph $f$ and $g ( x ) = \frac { 1 } { 2 } x - \frac { 11 } { 4 }$ , on the same screen, to show that they have the same end behavior.