Question 1045196
Not what you mean:    r(x)=x^3-8/x-2


What you mean but in pure text still:   r(x)=(x^3-8)/(x-2)


With rendering tags placed:  {{{r(x)=(x^3-8)/(x-2)}}}


{{{r(x)=((x-2)(x^2+2x+4))/(x-2)}}}
almost same as the simpler  {{{f(x)=x^2+2x+4}}}  but no point ( a hole) for x at 2.


No vertical asymptote
No horizontal asymptote
No oblique asymptote because function just like {{{y=x^2+2x+4}}} but with one point missing.



Critical x value is  at 2.
What about any roots for {{{x^2+2x+4}}}?
zeros for {{{x=(-2+- sqrt(4-4*4))/2}}}------Imaginary - no real roots


You can examine unbounded behavior but....


And no x intercepts
  

Let x=0, and find what is y; the vertical axis intercept.

{{{graph(400,400,-8,8,-2,14,(x^3-8)/(x-2))}}}