alleryStart learning →For f(x) = (6x squared + 5) divided by (3x squared - x + 2), what is the horizontal asymptote?
Ay = 3
By = 0
Cy = 2
Dy = 6
Answer & Solution
Correct answer: C. y = 2
1. Compare the degree of the top with the degree of the bottom.
2. Both are degree 2, so the asymptote is the ratio of the leading coefficients.
3. That ratio is 6 divided by 3, which is 2, so the asymptote is y = 2.
4. Answering y = 0 would apply the rule for a numerator of lower degree instead.
_Source: OpenStax Precalculus (CC BY 4.0), section 3.7 Rational Functions_
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