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Write the equation of all horizontal asymptotes of the function .
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Q. Write the equation of all horizontal asymptotes of the function .
- Question Prompt: Question Prompt: Determine the equation of all horizontal asymptotes for the function .
- Analyze Degrees: Analyze the degrees of the polynomials in the numerator and the denominator. The numerator has terms and , where grows faster than any polynomial. The denominator has terms and , with the highest degree being .
- Determine Asymptote: Since the highest degree in the denominator () is greater than the highest degree in the numerator (, considering as exponential growth), the horizontal asymptote is . This is because as approaches infinity, the polynomial term of higher degree in the denominator dominates, making the fraction approach zero.
