Question 259396
Vertical asymptotes occur when the denominator equals zero.
{{{x-3=0}}}
{{{x=3}}}
Look at the degree of x in the numerator and denominator.
{{{f(x)=x/(x-3)}}}
Divide numerator and denominator by x.
{{{f(x)=1/(1-3/x)}}} Now as x goes to {{{infinity}}} the term {{{3/x}}} goes to zero and {{{f(x)}}} looks like {{{f(x)=1}}}
So then the horizontal asymptote is 
{{{y=1}}}
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{{{drawing( 300, 300, -20, 20, -5, 5,grid( 1 ),
green(line(-20,1,20,1)),
green(line(3,-20,3,20)),
graph( 300, 300, -20, 20, -5, 5, x/(x-3))) }}}