Part (c)

y[x_]:=(x^3+2)/(x^2+4)

Plot[{y[x],x},{x,-10,10},PlotPoints->1000]

{Limit[y[x],x->-Infinity],Limit[y[x],x->Infinity]}

Vertical asymptotes: None
Horizontal asymptotes: None
Slanted asymptote: y = x