What does the acronym for horizontal asymptotes represent?

The correct answer highlights the conditions known as "Bottom heavy" or "Top heavy" when discussing horizontal asymptotes in rational functions. When analyzing a rational function, which is typically a fraction where both the numerator and the denominator are polynomials, the degrees of these polynomials play a crucial role in determining the behavior of the function as it approaches infinity or negative infinity.

If the degree of the numerator (top polynomial) is less than the degree of the denominator (bottom polynomial), the function will approach zero as opposed to exhibiting significant values—this is referred to as "bottom heavy." Conversely, if the degree of the numerator is greater than that of the denominator, the function will grow indefinitely, which is termed "top heavy." When both degrees are equal, the horizontal asymptote can be determined by the ratio of the leading coefficients of the polynomials.

Understanding these conditions is vital for predicting the end behavior of functions and identifying their horizontal asymptotes accurately. Hence, this answer captures the essential criteria that dictate the existence and positioning of horizontal asymptotes in rational expressions.