Are you allowed to take food on the airplane?

Usually you can take food for consumption on domestic flights. For foods you wish to carry-on, you must purchase them at the airport AFTER you have passed through security. The same goes for drinks. In larger airports, once you've passed through checkpoint, there will usually be a large variety of food shops and restaurants to choose from. In smaller airports, the options are much smaller; possibly none at all.

If you wish to take foods along that you have purchased at home, those foods must be packied in your checked-in bags and cannot be taken on the plane in your carry-on.
Food is allowed on airplanes, however "where you got the food" is the real question. Most airlines will not allow any kind of foodstuffs to be brought through the security checkpoint so any food you you want to bring onto the airplane has to be purchased beyond that point (and unless it's tax deductible you are better off eating before you get to the airport).