Does my iphone 4s automatically connect to Wi-Fi whenever I'm at home?

I'm pretty sure it says 3G at the top when I'm not at home, but when I'm, it has the 4 bar things. I have entered the code, but I don't have to do it every time, do I?

It will automatically connect when you're at home.

Your iPhone should reconnect automatically anytime a network you have entered is within range.

3G is cellular service and the 4 Bars are Wi-Fi.

Ok. This should help you out. 3G is always on because it's connected around your country and possible the whole world depending on your carrier. Your phone will connect to your Wi-Fi ONLY if you turned your Wi-Fi on, have entered the code previously, and within range of the connection. Since you have entered the password already, if you have your Wi-Fi on it will automatically connect when you're at home. However, this is not advised because if you turn your Wi-Fi on at all times, it'll search for connections everywhere you go. Thus, reducing battery life by a lot.