I wrote an answer to a similar question recently. See
What_would_you_use_to_determine_a_graph_is_a_function
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Yes. A graphing calculator has lots of options for mathematical calculations, but in addition, it has a relatively large screen, and options to graph functions.
the domain value is the x coordinate, and the range is the y coordinate. after graphing, do the vertical-line-test to see if it is a function or not.
Here is a great site that will tell you everything you know about graphing calculator programming, and its got programs there to! See the related link, "Graphing Calculator Programming".
Yes you can buy a graphing calculator. I know they are sold at places like Walmart, and Target and most of them are around $100 but go on sale before school starts for around $90. TI-83 and TI-84 graphing calculators are really good.
They are the same.