# How do you find the asymptotes for f(x)=(5x^3-9x^2-6x-4)/(-6x^2-9x-7)?

Dec 24, 2016

Slant asymptote: $y = - \frac{5}{6} x + \frac{11}{4}$.See the illustrative Socratic graph, for both the curve and the asymptote.

#### Explanation:

By actual division,

$y = - \frac{5}{6} x + \frac{11}{4} - \frac{\frac{155}{12} x + \frac{61}{4}}{6 {x}^{2} + 9 x + 7}$

$y = q o u t i e n t = = - \frac{5}{6} x + \frac{11}{4}$ gives the slant asymptote.

y-intercept ( x = 0 ) : 4/7

y-intercept ( x = 0 ): 3.44, nearly.

graph{(y-(4+6x+9x^2-5x^3)/(6x^2+9x+7))(y+5/6x-11/4)=0 [-10, 10, -10, 10]}