Multiple axis plot piecewise-defined function

I have this piecewise-defined function:

and I want to redefine the x axis, that now is a linspace vector, such that in the first trait ([0.25,0.25] to [0,0.5]) my x axis label, when I open the plot, goes from 0.25 to 0.5, the second one goes from 0.5 to 0 and the third one goes from 0 to 0.25. Is there a way to do this without redefining the function in three different coordinates' systems? Thanks

[dpb]

I don't follow the description, sorry. What's the data and form thereof that created the plot above and what, precisely, is wrong with it again?