Phone service will continue to work during an electrical outage as long as you are using a corded phone to make or receive a call within the eight hours battery life. 

Internet service can be accessed during battery backup if you are using a fully charged laptop that has an Ethernet cord plugged directly into the modem. 

Please note that the battery backup is intended for emergency use only.  Using it to make multiple or lengthy phone calls and/or using it to access the Internet can significantly decrease the original 8-hour battery life.