Question

Determine algebraically whether the graph of the function g is symmetric with respect to the x-axis, y-axis, or origin. g(x)=[(x^2)+(y^2)]^2=2xy

Answer 1

I would plot it. IF you have EXCEL, you can generate a plot.

http://images.google.com/imgres?imgurl=http://www.mccd.edu/faculty/powerd/M4c/M4c_Lab_Surface_files/image002.jpg&imgrefurl=http://www.mccd.edu/faculty/powerd/M4c/M4c_Lab_Surface.htm&h=288&w=388&sz=17&hl=en&start=1&sig2=9dJPuM8wbuHi73vSTKNr9A&um=1&usg=__5P5zcwrFpUZA7xffNrUr2BSqULc=&tbnid=k9n1el8mRJR8EM:&tbnh=91&tbnw=123&ei=bu3GSIj0MpvUMIjojSI&prev=/images%3Fq%3D)%253D%255B(x%255E2)%252B(y%255E2)%255D%255E2%253D2xy%2B%2B%2Bgraph%26um%3D1%26hl%3Den%26client%3Dfirefox-a%26rls%3Dorg.mozilla:en-US:official%26hs%3DYmV%26sa%3DN

In this, z=x^2 +y^2-2xy and you have it.