Question 1157588
{{{Q(x)=(3x^2-11x-4)/(2x^2-7x-4)}}}

Horizontal asymptote: 

find quotient of highest degree of variable

{{{3x^2/2x^2=3/2}}}

{{{(3x^2-11x-4)/(2x^2-7x-4)}}}->{{{3/2}}} as {{{x}}}-> ±{{{infinity}}}


Vertical asymptote:

find values excluded from domain

{{{2x^2-7x-4=0}}}

{{{(x-4)(2x+1)=0}}}

{{{x=4}}}

{{{2x=-1}}}->{{{x=-1/2}}}


{{{(3x^2-11x-4)/(2x^2-7x-4)}}}-> ±{{{infinity}}} as {{{x}}}->{{{-1/2}}}

{{{(3x^2-11x-4)/(2x^2-7x-4)}}}-> {{{undefined}}} as {{{x}}}->{{{4}}}

=> Vertical asymptote: {{{x=-1/2}}}

oblique​ asymptote:
since numerator and denominator have same highest degree of variable {{{x}}}, there is {{{no}}}{{{ oblique}}} asymptotes 


{{{drawing ( 600, 600, -10, 10, -10, 10,
green(line(-1/2,10,-1/2,-10)),
graph( 600, 600, -10, 10, -10, 10, 3/2,3/2, (3x^2-11x-4)/(2x^2-7x-4))) }}}