New raster layers can be created with on-the-fly processing by applying raster functions to raster datasets. If a copy of the new raster (function applied) is made and changes to the function on the copy or the original are made, both raster layers will be affected.
When copying/pasting a function layer in the table of contents, the layer is copied, but the in-memory function is not copied. Instead, the initial layer and the pasted layer both point to the same raster function in memory. As such, it is beneficial to think of the function as the source rather than a renderer option. Both layers then manipulate the same source function and a change in the function is seen in both layers.