Q: I have the IPhone 4S but, I don't have Air Play although I have downloaded both the new software updates for my IOS and Apple TV, how do I mirror my IOS to the Apple TV?

Welcome to the Apple Community.

Try the following steps, check whether things are working after each step where appropriate, before trying the next.

1. Check AirPlay is turned on on the Apple TV (turn it off and on if it already is)
2. Check that both devices are on the same network (Settings > Wifi, on the mobile device and Settings > General > Network, on the Apple TV).
3. Restart the Apple TV (Settings > General > Restart).
4. Restart the Apple TV by removing ALL the cables for 30 seconds.
5. Restart your router. (Also try removing it’s power cord for at least 30 seconds)
6. Restart your mobile device.

Basic AirPlay: Assuming both devices are on the same network and that AirPlay is not turned off on the Apple TV, then simply tap on the screen when you are watching content you wish to stream to your Apple TV, then tap the airplay icon that appears in the control bar, choose the Apple TV from the menu that appears.

Mirroring: When displaying the content you wish to mirror on the iPad 2 (or better), iPad Mini, iPhone 4S (or better), swipe from the bottom of the screen, tap the AirPlay icon and choose your Apple TV from the list of devices (iOS 7 or better) or double tap the home button (quickly) and swipe the bottom row of apps to the right to reveal the playback controls, tap the AirPlay icon and select your Apple TV from the list of available devices (pre-iOS7)