Question 712284: I am not sure if I am in the right place, but I need help my problem is:
Test the equation for symmetry with respect to the x-axis, the y-axis, and the orgin
x^2+xy^2+2y=1
Is it:
A. Symmetric with respect to the x-axis
B. Symmetric with respect to the y-axis
C. Symmetric with respect to the orgin
D. Symmetric with respect to the x-axis, the y-axis, and the origin.
Thank you for any help you can give me.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! If it was symmetrical with respect to the x-axis, then replacing each 'y' with '-y' should have no effect on the outcome
x^2+xy^2+2y=1
x^2+x(-y)^2+2(-y)=1
x^2+xy^2-2y=1 ... notice the change
Since there's a change, the first and last equations are NOT the same. So x^2+xy^2+2y=1 is NOT symmetric with respect to the x-axis
Similarly, if you replace each x with -x, you go from x^2+xy^2+2y=1 to x^2-xy^2+2y=1, which changes. So x^2+xy^2+2y=1 is NOT symmetric with respect to the y-axis
Because it's not symmetric with respect to either axis, it's NOT symmetric with respect to the origin
So it looks like none of the answer choices are correct. So there has to be something missing or there must be a typo somewhere. Please double check. Thanks.
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