Apple → apple tv and iTunes radio airplay

I thought that it was possible to open up iTunes Radio on your iPad or iPhone and airplay it to your Apple TV. I didn't see the option for it. Kind of stinks if you are in one room and want to change the station on the Apple TV you have to be in front of the TV and change it on the Apple TV interface.
How about music that you download from iTunes onto an iPad or iPhone? Can you airplay it to an Apple TV?

AirPlay options should be available by swiping up from the bottom of your device (iOS7). You can then select your device from there.

You can also, in the case of iTunes Radio, use the Remote app (must have latest version) to control Radio within iTunes and then select an AirPlay device(s) from within the Remote app itself.

The Remote App will control the apple tv directly as well.

True.