A function \$$f\colon \mathbb{R}\to\mathbb{R}\$$ is

1. _order-preserving_ if \$$x\leq y\$$ implies \$$f(x)\leq f(y)\$$, for all \$$x,y\in\mathbb{R}\$$;
2. _metric-preserving_ if \$$|x-y|=|f(x)-f(y)|\$$;
3. _addition-preserving_ if \$$f(x+y)=f(x)+f(y)\$$.

In each of the three cases above, find an \$$f\$$ that is _foo_-preserving and an example of an \$$f\$$ that is not _foo_-preserving.