1. \\(f(x)=e^x\\) is order-preserving, \\(f(x)=e^{x^2}\\) is not. \\(f(x)=e^x\\) also has the nice property that makes using a slide rule possible: \\(f(x+y)=f(x)*f(y)\\)

2. \\(f(x)=-x\\) is metric-preserving, as Dan and William mentioned.

3. I am not feeling up to the challenge of Cauchy right now.