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Yes.

Think of a function that starts at the origin, increases rapidly at first and then decays gradually to an asymptotic value of 0. It will have attained its asymptotic value at the start.

For example, the Fisher F distribution, which is often used, in statistics, to test the significance of regression coefficients. Follow the link for more on the F distribution.

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Q: Is it possible for a function that has a horizontal asymptote to attain the value of an asymptote?
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