Moral Relativism

In Ancient Rome, infanticide was a commonly accepted practice (the killing of an "undesirable" newborn child). In the United States today, infanticide is widely considered to be morally wrong. If moral relativism is true, then there's no objective truth of the matter about whether infanticide is wrong - infanticide was okay for the early Romans, but it's not okay today in the U.S.: both cultures' moral judgments are correct. Does this sound right to you, that the morality of infanticide is relative to culture? Or do you believe that there is an objectively right answer to whether or not infanticide is okay? Why or why not?