The symmetry required is a symmetry about the origin (the point (0,0)), meaning that if we replace x by -x and y by -y we get the same function.
A. can't be because y= 3 becomes -y = 3.
B. can't be because -y=(-x)^2 is the same as -y = x^2 not equal to y=x^2
C. all functions has odd parity such that upon changing x to - x y goes to -y. So this is the correct answer.
D. y = |x| changes to - y = |-x| or -y= |x| not equal y=|x|
So the correct answer is C....
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