Question 678483
In general, the procedure for asymptotes is the following:

-set the denominator equal to zero and solve
        the {{{zeroes}}} (if any) are the vertical asymptotes
        everything else is the domain

-compare the degrees of the numerator and the denominator
        if the degrees are the same, then you have a horizontal asymptote at 

y = (numerator's leading coefficient) / (denominator's leading coefficient)
        

if the denominator's degree is greater (by any margin), then you have a horizontal asymptote at {{{y = 0}}} (the x-axis)

        if the numerator's degree is greater (by a margin of 1), then you have a slant asymptote which you will find by doing long division


{{{y=1/(x-2)}}}

The vertical asymptotes (and any restrictions on the domain) come from the zeroes of the denominator, so I'll set the denominator equal to zero and solve.

{{{(x-2)=0}}}...=>...{{{x=2}}}.....so, domain is all {{{x <> 2 }}}

horizontal asymptote:  {{{y = 0}}} (the x-axis)


 {{{ graph( 600, 600, -10, 10, -10, 10, 1/(x-2),0) }}}

and you can draw a line parallel to {{{y-axis}}} through the point {{{x=2}}}