Graphing Calculators will be used to investigate complicated graphs and large calculations.  They are used for the entire course and the AP exam.  Additionally the graphing calculators are an important tool in subsequent mathematics courses (Calculus and Statistics).  

I will be conducting lessons using a TI-84 CE.  Other TI models are very good as well.  TI-84 has similar buttons to the TI-83. I am less familiar with the TI-89 and TI-nspire.  Therefore, if you purchase either of those models, you will be on your own.  Here is a link to AP's guidelines for calculators.  When purchasing a calculator consider what your AP Science teacher recommends as well.