How to know if there is a horizontal asymptote?
Understand the Problem
The question is asking about the conditions or rules that determine the existence of horizontal asymptotes in mathematical functions, specifically in the context of calculus and graph behavior at infinity.
Answer
Based on the degrees of the numerator and denominator
The final answer is based on the degrees of the numerator and denominator
Answer for screen readers
The final answer is based on the degrees of the numerator and denominator
More Information
Horizontal asymptotes can be determined using the degrees of the polynomials in the numerator and denominator. Specifically:
- If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y=0.
- If the degrees are equal, the asymptote is y=c, where c is the ratio of the leading coefficients.
Tips
A common mistake is confusing horizontal asymptotes with slant (oblique) asymptotes which occur when the degree of the numerator is exactly one more than the degree of the denominator.
Sources
- Identify horizontal asymptotes | College Algebra - courses.lumenlearning.com
- Horizontal Asymptote Rules | Study.com - study.com
- How to Find Horizontal Asymptotes of a Rational Function - wikiHow - wikihow.com
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