Question

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

Answer 1

Slant asymptote: `y =-5/6x+11/4`.See the illustrative Socratic graph, for both the curve and the asymptote.

Explanation:

By actual division,

`y =-5/6x+11/4-(155/12x+61/4)/(6x^2+9x+7)`

`y = qoutient = =-5/6x+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]}