Find the equation of the slant asymptote, if any. $r ( x ) = \frac { 2 x ^ { 2 } - 6 x - 7 } { x - 4 }$
A) $y = \frac { 1 } { x - 4 }$
B) $y = 2 x + 2$
C) $x = 2 y + 2$
D) $y = 2 x - 2$
E) $\text { no slant asymptote }$

Question

Quizplus · Accepted Answer

To find the slant (oblique) asymptote of the rational function $r(x) = \frac{2x^2 - 6x - 7}{x - 4}$, we perform polynomial long division or synthetic division. The quotient (ignoring the remainder) gives the equation of the slant asymptote. Dividing $2x^2 - 6x - 7$ by $x - 4$ yields a quotient of $2x + 2$, which corresponds to the equation $y = 2x + 2$.

Find the Equation of the Slant Asymptote, If Any r(x)=2x2−6x−7x−4r ( x ) = \frac { 2 x ^ { 2 } - 6 x - 7 } { x - 4 }r(x)=x−42x2−6x−7​

Find the Equation of the Slant Asymptote, If Any $r ( x ) = \frac { 2 x ^ { 2 } - 6 x - 7 } { x - 4 }$