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.

x = -5

step-by-step explanation: