Let $f(x)$ be a [function](https://artofproblemsolving.com/wiki/index.php/Function) with the two properties:

(a) for any two real numbers $x$ and $y$, $f(x+y) = x + f(y)$, and
(b) $f(0) = 2$.
What is the value of $f(1998)$?
$\mathrm{(A)}\ 0  \qquad\mathrm{(B)}\ 2  \qquad\mathrm{(C)}\ 1996 \qquad\mathrm{(D)}\ 1998  \qquad\mathrm{(E)}\ 2000$
\[f(1998 + 0) = 1998 + f(0) = 2000 \Rightarrow \mathrm{(E)}\]
The function $f(x) = x+2$ satisfies these properties.