Question

Which statement is true if the degree of the numerator's polynomial function is greater than the degree of the denominator's polynomial function? A. it has one horizontal asymptote. B. it has one vertical asymtote. C. it has no horizontal asymptote. D. it has no vertical asymptote

Answer 1

Option: C is the correct answer.

C. It has no horizontal asymptote.

Explanation:

We know that the horizontal asymptote of a function is obtained as follows:

1)

if the degree of the numerator and denominator are equal then we divide the coefficients of the higher degree term.

2)

If the degree of denominator term is greater than the numerator than the horizontal asymptote is the x-axis.

3)

Also if the numerator is of greater degree as compared to the denominator there are no horizontal asymptote.

Hence, in the given question we are given 3) case.

Hence, there are no horizontal asymptote.

Answer 2

If the degree of the numerator`s polynomial function is greater than the degree of the denominator`s polynomial function than:
lim f ( x ) = ∞
x→∞
Answer:
C ) it has no horizontal asymptote.