answered
2014-07-09 12:16:25 -0600
I also got the following (I have verified this with a 3D graphing program but it still may be incorrect):
c | d
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e | f
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b | a
I will go through each letter and show you my thought process behind matching them.
(a) $x^2 -y^2$ automatically triggers a reaction in my head that tells me I should look for a hyperbola. The only graph we have that has a hyperbola inside of it is the bottom right.
(b) This was actually one of the more tricky ones. I decided to compare this to a slightly more simple function, $1\big/(x^2+y^2)$ since $-1 \leq \sin(x^2 + y^2) \leq 1$. Generally, $\pm1$ divided by anything should be very large near zero and eventually die down the farther out you go. The bottom left graph fits this description.
(c) The graph of $z$ should always be bounded by $-1 \leq z \leq 1$ and have some waves in it. The top left graph fits this description.
(d) Setting $f(x, y) = 0$ and solving for $y$, we obtain $y = -2x$. Setting $f(x, y) = c$ yields different transformations of this equation and creates a contour plot like that shown in the top right graph.
(e) This graph should be similar to (d) but with more waves. You can think of it as a wavy plane (I believe that this type of equation was once described as a "wavy wall" in our class). A graph that is similar to (d) but has more waves is the middle left.
(f) This leaves one final graph, but I will describe how I figured this one out as well. Setting $f(x, y) = 0$ and solving for $x$, we obtain $x = y^2$. This is a horizontal parabola. Setting $f(x, y) = c$ yields different transformations of this equation and creates a contour plot like that shown in the middle right graph.
