There are 3 cases to consider when determining horizontal asymptotes:
1) Case 1:
if: degree of numerator < degree of denominator
then: horizontal asymptote: y = 0 (x-axis)
i.e.f(x)=bx5+......ax3+......→ horizontal asymptote: y=0
2) Case 2:
if: degree of numerator = degree of denominator
then: horizontal asymptote: y = leadingcoefficientofdenominatorleadingcoefficientofnumerator
i.e.f(x)=bx5+......ax5+......→ horizontal asymptote: y=ba
3) Case 3:
if: degree of numerator > degree of denominator
then: horizontal asymptote: NONE
i.e.f(x)=bx3+......ax5+......→NOhorizontalasymptote