Quiz 2 Solutions

The only two functions which possess circular symmetry are B and D. Since D is undefined at the origin and is always les than zero, we see that graph 4 is a picture of D. The only other graph with circular symmetry is 5 which also has the periodic structure required of B.

Function C is a cylinder in the sense that it lacks dependence on the variable x. In the y direction the graph should be periodic like $\cos y$ so graph 9 is the correct choice.

Since the contours of the function G are hyperbolas and the function is 1 along the lines x = 0 and y=0, we see that graph 7 is the only correct choice.

Function H also has hyperbolas for contours, but in this case z is greater than or equal to zero. Since z=0 along the lines x=0 and y=0 we see that graph 2 is the correct choice.

Function E is always positive and is periodic in both x and y so graph 3 is correct.

Of the remaining graphs and functions, graph 8 almost has circular symmetry (it's actually elliptical.) Also, this graph has ``wiggles'' that might be caused be sine or cosine. Thus, this must be the graph of function F.

We are left with graphs 1 and 6 and functions A and I. Notice that function I is always positive and graph 1 is also positive. Also, function A is negative whenever xy<0. This occurs in quadrants II and IV in the xy-plane. So we have as our answers

1-I, 2-H, 3-E, 4-D, 5-B, 6-A, 7-G, 8-F, 9-C;

A-6, B-5, C-9, D-4, E-3, F-8, G-7, H-2, I-1.