Overview 
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The graph tool is capable of graphing a wide variety of functions and relations. Uniquely, you do not have to "tell" the graph tool what sort of function to graph, the graph tool automatically determines this for itself based on what you type.
For example: If you type a function which only includes the variable x, the graph tool will graph a Cartesian function. If you include y' in the expression, it will automatically graph a direction field. Functions defined implicitly will automatically be rearranged into Cartesian or inverse Cartesian functions if this is possible. You only have to worry about what to graph rather than how to graph it.
The next sections discuss the different types of things that the graph tool can graph and how to enter them.
