In some cases, when applying a renderer function to an image, the renderer function does not have the same range as the image. The situation results in the image displayed in the Preview window differing from the image published from ArcMap. This issue tends to happen when the renderer function is generated from different raster data.
However, it is possible to apply a renderer function chain to images of different pixel ranges. The stretch values and the color ramp of a raster can be saved by exporting the raster function template in the Layer Properties window as described in the following documentation: ArcMap: Saving a raster's function template from the layer's symbology. To generate a renderer function chain applicable to images of different pixel ranges, create a placeholder raster dataset that covers the maximum and minimum values of all the other raster datasets and create the raster processing template.