Cameron Diaz and Alex Rodriguez stepped out in Miami yesterday to do lunch and check in on the construction of a home they're rumored to be building together. She headed to Florida following a busy LA Sunday, which kicked off with press duties for her upcoming comedy Bad Teacher and wrapped up at the MTV Movie Awards. Cameron took the stage at the show with her hilarious costar Jason Segel before retiring to the MTV Movie Awards afterparty at Soho House, where Alex joined her. It seems she and Alex are going strong despite rumors last week that they'd parted ways. Both Alex and Cameron are busy with their respective work duties. He's in the midst of a time-consuming season with the Yankees, and she's on the press trail ahead of the release of her and Jason's movie on June 24. Cameron was also just in London shooting Gambit with Colin Firth.