y[x_]:=3*x^(-1/2)+x/2-5
Plot[{y[x],x/2-5},{x,0,20},PlotRange->{-6,6},PlotPoints->1000]
Limit[y[x],x->0,Direction->-1]
Limit[y[x]-x/2+5,x->Infinity]
Vertical asymptote: x = 0
Horizontal asymptotes: None
Slanted asymptote: y = x/2 - 5