Would something like this work?

 Plot[Round[n], {n, -3, 3}, 
 Ticks -> {Transpose[{Range[7] - 3, Q (Range[7] - 3)}], 
 Transpose[{Range[7] - 3, Q (Range[7] - 3)}]}, 
 AspectRatio -> Automatic, ExclusionsStyle -> Opacity[1], 
 AxesLabel -> {Input, "Output"}]

![enter image description here][1]


 [1]: https://i.sstatic.net/biNom.png