Desmos is a free graphing calculator that has been available for a few years as a browser-based tool and as an iPad app. Late last month Desmos launched a free Android app.
The Desmos calculator performs all of the functions you would expect to see in a graphing calculator with a couple of extras that you don't find in typical graphing calculators. Desmos allows you to share your equations and graphs. Desmos graphs your equations as you type them and redraws them as you alter your equations. See some of the best features of Desmos in the videos embedded below.
The Android app will work without an internet connection nor do all of the sharing features work on Android version.