Let $f:\mathbb{R}\to \mathbb{R}$ be a function such that $f(x+y)=f(x)+f(y)$ for all $x,y\in \mathbb{R}$. If the relation $R$ is defined by $xRy$ if $f(x)=f(y)$, then $R$ is:

1. A.An equivalence relation
2. B.Only reflexive and symmetric
3. C.Only symmetric and transitive
4. D.Not a relation