Question 1179885
assuming you have:


{{{y=sqrt(x-4)}}}->  is asymptotic to {{{x =y^2+4}}}


{{{y=2x+4}}}-> this is linear equation, so line doesn't have a vertical asymptote


{{{y= 1/(x-4)}}}->is asymptotic to {{{x = 4}}} and is asymptotic to {{{y = 0}}}


{{{y=(x-4)^2}}}->is asymptotic to {{{x=sqrt(y)}}}



so, answer is: {{{y = 1/(x-4)}}}-has a vertical asymptote at {{{x =4}}}


{{{drawing( 600, 600, -10,10, -10, 10, 
blue(line(4,-10,4,10)),
 graph( 600, 600, -10,10, -10, 10,1/(x-4) ,1/(x-4))) }}}