Find the slant asymptote of the rational function .

Question

Find the slant asymptote of the rational function  .

Quizplus · Accepted Answer

To find the slant asymptote of a rational function, divide the numerator by the denominator using long division or synthetic division. The quotient will be the equation of the slant asymptote. Performing synthetic division, we get:

\begin{array}{c|ccccc}
& 11e & -7b & 6 & b & 14 \ \cline{2-6}
7 & & 11e & -31b & 215 & -202b & \ \cline{2-6}
& & & -7b & 215-(-31b) & -202b \ 
\end{array}

So the quotient is 11e-7b+ \frac{215-(-31b)}{7b-6}. As the degree of the numerator is one more than the degree of the denominator, the slant asymptote is a line with slope 11e/7 and y-intercept -7e/7 or -e. Therefore, the equation of the slant asymptote is y = \frac{11}{7}x - e. The only choice that matches this equation is (D).

Find the Slant Asymptote of the Rational Function