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