I recently returned to school after a long hiatus. While learning pre-calc and calculus, I found Quick Graph for iOS to be the best graphing calculator. It graphs both 2D and 3D functions. The app also handles multiple functions which are allocated different colors automatically. Unlike stand-alone calculators you can zoom in and out with standard pinch gestures, and in 3D you can rotate the graph in any direction. It also helps that the interface is intuitive: for instance to change the color of your function, there is a little arrow bullet in your current color next to your function in the function list: you just click it and it opens a color selection dialog.
The free version is very functional and has no ads or annoyances. The full version gives extra features such as unlimited functions (free is limited to 6) and tracing the graph by tap and hold (it is easy estimate the same data in the free version, but it won’t give you the exact value).
Unfortunately, my iPhone broke and I am now using Android on which I have not found a graphing app of the same level of intuitive design.
[Note: If you're in school, make sure to check with your professor before trying to use an iPhone application like this on a test as I know many programs mandate the use of a stand alone calculator.--OH]
If anyone has a recommendation for a solid graphing application on Android please let us know and I'll add it to the review! --OH