Use the techniques we discussed in class today to analyze the graph of
the function
$$f(x,y) = x^2-y^2.$$
Be as precise as you can about your conclusions and your reasoning, and be
sure to describe your final result. Sketch the graph carefully. Use a
domain with $x$ in the interval $[-1,1]$ and $y$ in the interval $[-1,1]$
(with the interval for $z$ chosen appropriately). Make sure you label the
axes in your final drawing, and be sure that it is at least three inches
by three inches in size.
Do the best you can. I know this is new for you, but it takes practice,
and so you have to start somewhere. Do not just look this up on the
internet or graph it on your calculator or computer. The whole point is to
be able to understand a complicated object by breaking it down into less
complicated pieces. You loose the whole benefit of this practice if you
don't go through that process.
We will do more with this on Friday in class, so be sure to try this
before then. That is part of your preparation for class.
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