Find all vertical and horizontal asymptotes of the graph of

Find all vertical and horizontal asymptotes of the graph of the given function. g(x) = 5x^2/x^2 - 3x-4

Solution

given g(x)=5x²_/(x²-3x-4)

horizontal asymptote

y =lim_x->5x²_/(x²-3x-4)

y =lim_x->5x²_{/(x²(1-(3/x)-(4/x²)))}

y =lim_x->5_{/(1-(3/x)-(4/x²))}

y =5_/(1-(0)-(0))

y=5_/1

y=5

horizontal asymptote is y =5

for vertical asymptote :

g(x)=5x²_/(x²-3x-4)

g(x)=5x²_{/((x-4)(x+1))}

denominator =0

(x-4)(x+1)=0

=>x=-1, x=4

vertical asymptotes are x =-1,x =4