Let $f:\mathbb{R}^{2}\rightarrow \mathbb{R}$ be a continuous map such that $f(x) = 0$ for only finitely many values of $x$. Which of the following is true?
- Either $f(x)\leq 0$ for all $x$, or, $f(x) \geq 0$ for all $x$
- The map $f$ is onto
- The map $f$ is one-to-one
- None of the above