Question
Find the Horizontal Asymptote of this function…
Ask by Dawson Conner. in the United States
Jan 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
There is no horizontal asymptote for the function
.
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Extra Insights
To determine the horizontal asymptote of the function
, we need to look at the degrees of the numerator and the denominator. The highest degree in the numerator is 3 (from
), and the highest degree in the denominator is 1 (from
). Since the degree of the numerator (3) is greater than the degree of the denominator (1), there is no horizontal asymptote for this function. Instead, the function will display polynomial growth as
approaches infinity.
As a fun fact, when dealing with rational functions, if the degree of the numerator is less than the degree of the denominator, then the horizontal asymptote is
. And if the degrees are the same, the horizontal asymptote can be found by taking the ratio of the leading coefficients. This helps you visualize how the function behaves at extreme values of
!