TITLE: how do you graph a function?
QUESTION [8 upvotes]: I know techniques from calculus to more or less know the behavior of a function. But I still don't know how to graph functions people expect me to graph, for example, in Fulton's curve book there are curves like $F=(X^2+Y^2)^3-4x^2y^2$ and there's a picture but if someone asked me to draw such function I've had no idea where to start. In summary I'm asking what do you do when you want to do the graph of a function (of one or several real variables), please don't skip anything, I think I lack of some things that are obvious for others but not for me. Regards.

REPLY [4 votes]: The following freely available books are good references for this sort of thing, if you are interested in pursuing the topic in spite of what others have said.
R. Howard Duncan, Practical Curve Tracing with Chapters on Differentiation and Integration (1910)
Percival Frost, An Elementary Treatise on Curve Tracing (1918)
William Woolsey Johnson, Curve Tracing in Cartesian Coordinates (1884)