http://calc3.askbot.com/questions/Open source question and answer forum written in Python and DjangoenCopyright Askbot, 2010-2011.Wed, 09 Jul 2014 12:16:25 -0500http://calc3.askbot.com/question/67/how-do-i-match-the-groovy-equations-with-the-groovy-pictures/The in class worksheet from Tuesday, July 8th, had several functions to match with the images on the back. I am having trouble matching them all. I would like to post the answers I think are correct and wait for others to respond with theirs. Any tips on matching them would be great! If you visualize the images on the back as a matrix, my answers are as follows C D E F B A Thanks... COMMENT: I don't think we can edit anyone else's post, only our own. At least I can't...Tiffany, all I did was use the space bar and it auto gave be the cool box! Wed, 09 Jul 2014 09:46:23 -0500http://calc3.askbot.com/question/67/how-do-i-match-the-groovy-equations-with-the-groovy-pictures/http://calc3.askbot.com/question/67/how-do-i-match-the-groovy-equations-with-the-groovy-pictures/?answer=70#post-id-70I also got the following (I have verified this with a 3D graphing program but it still may be incorrect): c | d ---*--- e | f ---*--- 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.Wed, 09 Jul 2014 12:16:25 -0500http://calc3.askbot.com/question/67/how-do-i-match-the-groovy-equations-with-the-groovy-pictures/?answer=70#post-id-70http://calc3.askbot.com/question/67/how-do-i-match-the-groovy-equations-with-the-groovy-pictures/?answer=68#post-id-68I got b d e f c a ( Following the same order as yours, I can't figure out how to space them like you, and only have a short break in my other class to type this! :) So I know our c and b are the only two that are different. I think the first one is b since you've got the c / by a circle, which should fill the bowl that you see in the first picture. *Comment*: Looks good! If you hit the "edit" button, you can see exactly how Christina entered her question - a useful trick to see how folks format their work.Wed, 09 Jul 2014 10:42:34 -0500http://calc3.askbot.com/question/67/how-do-i-match-the-groovy-equations-with-the-groovy-pictures/?answer=68#post-id-68