I work in C++, so I might be looking for the history of

        Session::set_state (XMLNode const & node)

I would write:

        git log -L:set_state:session_state.cc

If I worked in C, and I had this in a file:

        void
        some_function_name (type1_t t1, type2_t t2)

I would write

        git log -L:some_function_name:thefile.cc