Determine whether the function below has any horizontal asymptotes.
A) horizontal asymptotes:
B) no horizontal asymptotes
C) horizontal asymptotes:
D) horizontal asymptotes:
E) horizontal asymptotes:

Question

​Determine whether the function below has any horizontal asymptotes. ​  ​
A) ​horizontal asymptotes: 
B) ​no horizontal asymptotes 
C) ​horizontal asymptotes: 
D) ​horizontal asymptotes: 
E) ​​horizontal asymptotes:

Quizplus · Accepted Answer

The function does not have any horizontal asymptotes because the degree of the numerator (5) and the degree of the denominator (2) are not equal. When the degree of the numerator is less than the degree of the denominator, there is a horizontal asymptote at y=0. When the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote. Instead, there is a slant asymptote. When the degree of the numerator is equal to the degree of the denominator, there may or may not be a horizontal asymptote, depending on the coefficients of the leading terms.

​Determine Whether the Function Below Has Any Horizontal Asymptotes

Determine Whether the Function Below Has Any Horizontal Asymptotes