WASHINGTON — The Supreme Court is taking on a major test of LGBT rights in cases that look at whether federal civil rights law bans job discrimination on the basis of sexual orientation and gender identity.

The justices said Monday they will hear cases involving people who claim they were fired because of their sexual orientation and another that involves a funeral home employee who was fired after disclosing that she was transitioning from male to female and dressed as a woman.

The cases will be argued in the fall, with decisions likely by June 2020.

The issue is whether Title VII of the federal Civil Rights Act of 1964, which prohibits sex discrimination, protects LGBT people from job discrimination. Title VII does not specifically mention sexual orientation or transgender status, but federal appeals courts in Chicago and New York have ruled recently that gay and lesbian employees are entitled to protection from discrimination. The federal appeals court in Cincinnati has extended similar protections for transgender people.

The justices will take up three cases in the fall.

In one, the federal appeals court in New York ruled in favor of a gay skydiving instructor who claimed he was fired because of his sexual orientation. The full 2nd U.S. Circuit Court of Appeals ruled 10-3 that it was abandoning its earlier holding that Title VII didn’t cover sexual orientation because “legal doctrine evolves.”

The second case is from Georgia, where the federal appeals court ruled against a gay employee of Clayton County, in the Atlanta suburbs. Gerald Bostock claimed he was fired in 2013 because he is gay. The county argues that Bostock was let go because of the results of an audit of funds he managed.

The third case comes from Michigan, where a funeral home fired a transgender woman. The appeals court in Cincinnati ruled that the firing constituted sex discrimination under federal law.