How can material assignments to a joined mesh be changed after the meshes are joined?

Example: Create a scene with a cube and sphere. Assign material #1 to the cube and material #2 to the sphere. Select the cube and the sphere, using crtl-J join the meshes. The result is shown below.

The material panel for this joined object shows both materials.

If edit mode is entered, the there is an assign, select, and deselect option, but its not clear how to use this to change the mesh material assignments.

What is the procedure to change the material mesh assignment? For example, how is the red material assigned to one face of the cube?

Example blender file: