Chapter 1 - Limits and Continuity - 1.3 Limits At Infinity; End Behavior Of A Function - Exercises Set 1.3 - Page 79: 34

False.

Of course, if both limits are true, $y=L$ is a horizontal asymptote, but to be one, only one of the limits needs to be true. The correct statement should have "or" instead of "and": $\lim\limits_{x \to -\infty} f(x)=L$ or $\lim\limits_{x \to \infty} f(x)=L$