Here is my solution.

As William Godwin mentioned, the identity function \\(x \mapsto x\\) is order-, metric-, and addition-preserving.

1. \\(x \mapsto x+1\\) is order-preserving, but \\(x \mapsto x^2\\) is not.

2. \\(x \mapsto x-1\\) is metric-preserving, but \\(x \mapsto |x|\\) is not.

3. \\(x \mapsto 2x\\) is addition-preserving, but \\(x \mapsto x^3\\) is not.

As William Godwin mentioned, the identity function \\(x \mapsto x\\) is order-, metric-, and addition-preserving.

1. \\(x \mapsto x+1\\) is order-preserving, but \\(x \mapsto x^2\\) is not.

2. \\(x \mapsto x-1\\) is metric-preserving, but \\(x \mapsto |x|\\) is not.

3. \\(x \mapsto 2x\\) is addition-preserving, but \\(x \mapsto x^3\\) is not.