To find vertical asymptotes, set the denominator = 0



; 
;   

So the two vertical asymptotes are x=-3 and x=3.
We draw those.



Now we ind what you asked for, the oblique or curvilinear 
asymptotes.  To find that we use long division:

                x+0 
x²+0x-9)x³+0x²+0x-1
        x³+0x²-9x
           0x²+9x-1
           0x²+0x+0
               9x-1

and we can rewrite the equation: 





When x gets larger and larger in absolute value
the fraction gets closer and closer to 0, so to 
get the asymptote we drop the fraction and set 
y = the quotient only.

So we have an oblique asymptote, which has 
this equation: 



We draw it:



The we get some points

x|-10| -7 |  -5  |-3.5 |-2.5|
-|---|----|------|-----|-----
y|-11|-8.6|-7.875|-13.5|6.05|


x| 10 | 7  |   5  | 4 | 2.6|
-|----|----|------|---|-----
y|10.9|8.55| 7.75 | 9 |-7.4|

And sketch the graph:



Edwin