During which of these cases would you use polynomial long division to find the equation of a horizontal asymptote? A If the degree of the numerator is larger than the degree of the denominator. B If the degree of the numerator is the same as the degree of the denominator. C If the degree of the numerator is smaller than the degree of the denominator. D If the degree of the numerator is one larger than the degree of the denominator.

Option B and C

During these cases would you use polynomial long division to find the equation of a horizontal asymptote

Solution:

Given that, from a set of options we have to select cases which can be used to find the equations of a horizontal asymptote.

A) If the degree of the numerator is larger than the degree of the denominator.

The rational function f (x) = P (x) / Q (x) in lowest terms has no horizontal asymptotes if the degree of the numerator, P (x), is greater than the degree of denominator, Q (x).

B) If the degree of the numerator is the same as the degree of the denominator.

The rational function f (x) = P (x) / Q (x) in lowest terms has horizontal asymptote y = a / b if the degree of the numerator, P (x), is equal to the degree of denominator, Q (x), where a is the leading coefficient of P (x) and b is leading coefficient of Q (x). In this case, f (x) → a / b as x → ±∞.

C) If the degree of the numerator is smaller than the degree of the denominator.

The rational function f (x) = P (x) / Q (x) in lowest terms has horizontal asymptote

y = 0 if the degree of the numerator, P (x), is less than the degree of denominator, Q (x). In this case, f (x) → 0 as x → ±∞.

D) If the degree of the numerator is one larger than the degree of the denominator

The rational function f (x) = P (x) / Q (x) in lowest terms has no horizontal asymptotes if the degree of the numerator, P (x), is greater than the degree of denominator, Q (x).

Hence, options B and C are suitable.