Does Epsom sx435x support AirPrint?

That printer does not support AirPrint, as shown here:

http://support.apple.com/kb/HT4356

About the best you could do with that printer is download the (free) Epson iPrint app from the App Store. That is nowhere near as capable as AirPrint, but better than nothing.

If you do end up using Epson iPrint, I recommend you start by clicking "Maintenance" in the lower left, then (scroll down to) Printer Settings, which will open a page in Safari.

From the Safari page, choose "Firmware Updates" and that will update your printer to the latest firmware.