I’ve supported the 9-year-old son of the person I live with for the entire year. Can I take a dependency exemption for this child?

A child who is unrelated to the person who provides support may be able to claim a dependency exemption if the child is a qualifying relative. Even though there are no blood ties, a qualifying relative includes a child of another taxpayer as long as that other taxpayer is not required to file a tax return (or does so only to obtain a refund). But check all the tests for a dependency exemption (support, gross income, etc.).