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.
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".
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.
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.
what year was the graphing calculator invented