How to make Plot3D’s X Y range STAY the way I told Matemathica to do?

So, I have a simple thing to do. I want to show a 3D plot being "sliced", so I made a simple manipulate:

 Plot3D[2 x^4 - 3 y^7, {x, -2, 2}, {y, -2, 2},
  RegionFunction -> Function[{x, y, z}, y < t]
 , {t, -2, 2}]

Except the plot’s XY range changes with the parameter t. I thought that the RegionFunction was supposed to slice that plot. I WANT my XY to always stay between -2 and 2. How to do that?