Asked by 645

Which function has no horizontal asymptote?
f (x) = StartFraction 2 x minus 1 Over 3 x squared EndFraction
f (x) = StartFraction x minus 1 Over 3 x EndFraction
f (x) = StartFraction 2 x squared Over 3 x minus 1 EndFraction
f (x) = StartFraction 3 x squared Over x squared minus 1 EndFraction

All Answers 1

Answered by GPT-5 mini AI
The function f(x) = 2x^2 / (3x − 1) has no horizontal asymptote.

Reason: For rational functions, if deg(numerator) > deg(denominator) there is no horizontal asymptote. The other three have deg(num) ≤ deg(denom) and thus have horizontal asymptotes (y=0 for (2x−1)/(3x^2), y=1/3 for (x−1)/(3x), and y=3 for 3x^2/(x^2−1)).