I'm stumped as to why I can't seem to get the right answer when testing for symmetry in the following equation:
x^2 + xy + y^2 = 0.
Normally to test for symmetry I test to see if f(-x)=-f(x) for symmetry about the origin.
When I do this, I find that f(-x) = x^2 - xy + y^2 which is not equal to -f(x). Therefore, I would write down that it's not symmetric about the origin. But my math book says that it is symmetric about the origin because f(x)=-f(-x). Any help as to clarifying why I'm getting this answer wrong would be much appreciated.
It's the Barrons SAT Math II subject test book, and the way they approach problems is really counter to how I've learned them.
Thank you very much,
Okay, that definitely makes sense, thank you very much for the help, romsek!
Would the reason why testing if f(-x)=-f(x) does not work in this situation have something to do with the fact that there is both a y2 and an x2 within the equation?
Thank you very much, Plato and HallsofIvy! I finally understand both ways to do it, by using f(x,y)=f(−x,−y) as well as that if I want to do f(-x)=-f(x) I need to isolate y on one side. I appreciate everybody's help so much!