Cheap Software/Tools for Plotting Cartesian Graphs

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Does anyone know any cheap (preferably free) software or online tools for plotting reasonably complicated Cartesian graphs? I would like the functionality to 1) be able to select the range of x and y over which to view the graph, 2) be able to plot multiple functions on the same graph and 3) plot quite long functions of x and y (though they will not contain anything non-elementary). 2D only needed
 
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Gnuplot [1] may fit your bill and has been around for a long time (I used it for my papers and thesis ages ago).

[1] http://www.gnuplot.info/
 
Thanks for the recommendation. It seems to work for most things and there's loads of documentation but I haven't been able to get this online trial to plot my y-scale too? e.g. http://toycompute.net/?p=1 it's fine when I try code " plot x**2 " but, say, " plot x**2+y**2=6 " and it just plots y=x^2 again, rather than x^2+y^2=6. I couldn't find any example plots using full f(x,y) functions either. Any idea how to deal with this?
 
desmos.com is pretty good as long as you have a good connection to the internet.

edit: If you are looking to make images to publish, this will not do.
 
Geogebra

You should go on google and search for Geogebra. It is free, but you need to have jave on your computer, so that you can use Geogebra smoothly.