Three rules of horizontal asymptotes
When the top degree is less than the bottom degree the asymptote is the x axisWhen they are the same degrees, divide the coefficients top by bottom; the answer is the HAWhen the top degree is greater than bottom degree there is no HA
The three rules of horizontal asymptotes are as follows:
1. The horizontal asymptote of a rational function with a higher degree in the numerator than in the denominator is a slant asymptote, not a horizontal one.
2. If the degree of the denominator is greater than the degree of the numerator, then the horizontal asymptote is y = 0.
3. If the degree of the numerator and the denominator is the same, then the horizontal asymptote is y = ratio of the leading coefficients.
It’s important to note that these rules only apply to rational functions, which are functions that can be written as a ratio of two polynomials. Additionally, these rules assume that the function’s variables are approaching infinity or negative infinity, meaning that the function is leveling off as it gets very large or very small. If the function oscillates or behaves erratically, there may not be a horizontal asymptote or these rules may not apply.
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