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I am finding that visualizing those curves is not easy for me either. For some of them it helped me to first visualize what was going on in the x-y plane and then consider how the z affected that. But since the problems said to "investigate", I figured using wolfram alpha was a good tool. If you parametric plot them it gives an ok visual. At some point I want to learn how to use Mathematica for problems like these.

I am finding that visualizing those curves is not easy for me either. For some of them it helped me to first visualize what was going on in the x-y plane and then consider how the z affected that. But since the problems said to "investigate", I figured decided that using wolfram alpha was a good tool. idea. If you parametric plot them it gives an ok visual. At some point I want to learn how to use Mathematica for problems like these.