A rational function is one with a polynomial numerator and a polynomial
denominator.

If the degree of the numerator is LESS THAN the degree of the denominator,
the x-axis (y = 0) is the horizontal asymptote.

If the degree of the numerator IS EQUAL TO the degree of the denominator,
there is a horizontal asymptote at the line y = b, where the constant b is
determined by dividing the leading coefficient in the numerator by the
leading coefficient of the denominator.

To answer your question:

If the degree of the numerator is GREATER THAN the degree of the
denominator, there is NO horizontal asymptote.

Edwin