Answer
False.
Work Step by Step
No information was given about the nature of $f(x)$ and hence if $f(x)$ is not continuous over the interval, it does not necessarily have $2$ horizontal tangent lines.
For example $\tan{x}$ has infinitely many x-intercepts but no horizontal tangents lines since $\tan{x}$ is not continuous at $x=\frac{k}{2}\pi$ where $ k$ is any integer.
