Looking for tips on sketching of 3-d graphs?

[maximf]

basically I'm in the last 2 chapters of multi variable calculus (right now in double integrals) and i know how important it is in some exercises to sketch the 3-d graphs accuratley. However all the 3-d graphs that I'm trying to sketch are very off... even a simple shape like a cylinder looks bad.

anyway are there any tips for manual sketching that might help me graph the functions little more accuratley?

 

[HallsofIvy]

Drawing "level curves" should help. One thing I like to do is draw cross sections in the coordinate planes: if x= 0, what is the graph in the yz-plane? If y= 0, what is the graph in the xz-plane? If z= 0, what is the graph in the xy-plane? The imagine those graphs place on the coordinate axes.

 

[maximf]

how do you properly draw the coordinate axes? what i do is sketch one vertical that will be Z and one horizontal that will be Y. and the X axis i draw diagonally through the squares (i use math paper obviously...)

 

[Math Jeans]

Drawing "level curves" should help. One thing I like to do is draw cross sections in the coordinate planes: if x= 0, what is the graph in the yz-plane? If y= 0, what is the graph in the xz-plane? If z= 0, what is the graph in the xy-plane? The imagine those graphs place on the coordinate axes.

Yes. This is probably the best way to do it. Just substitute different values for the individual variables in the equation. This will give you the 2d graph created with the remaining variables on the plane perpendicular to the point at which you have substituted. Just do this a few times for all of the different variables and you will be able to shade in a complete 3d graph.

My teachers call it the trace method.