[Math] Can there be a non-polynomial continuous function from $\mathbb{R}$ to $\mathbb{R}$ that has multiple zero-valued points

Question

1) Is there any non-polynomial function from $\mathbb{R}$ to $\mathbb{R}$ that has more than one zero-valued point in domain?

2) Is there any non-polynomial function from $\mathbb{R}$ to $\mathbb{R}$ that has countable infinite number of zero-valued points?

Non-polynomial functions can have polynomial terms – but function must contain non-polynomial terms.

OOps. Excluding ones that can be expressed by Taylor series using $x=c$ where $c$ is some constant.

Answer 1

Sure: $f(x)=\sin x$, unless I’m completely misunderstanding the question.