xy=2 Is this? a)symmetry at x-axis,y-axis, and/or at the origin

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xy=2 Is this? a)symmetry at x-axis,y-axis, and/or at the origin

Precalculus
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rewrite as y = 2/x... recognize this?
yes
also if f(-x) = f(x) then it is symmetric about y. if f(-x) = -f(x) it is symmetric about the origin. if f(x) = y or -y then it is symmetric about x.

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not or, and.
that is, x: -> y and x -> -y then it is not a function but is symmetric about the x-axis.
trying to keep up but im sure y=2/x is a function and i wanted to know if any of the combinations of symmetry x-axis,y-axis,origin(or just at least one of these) are possible
learn to do this: \[f(x) = \frac{ 2 }{ x }\Rightarrow f(-x) = \frac{ 2 }{ -x }=-\frac{ 2 }{ x }\Rightarrow f(-x) = -f(x)\] so it's symmetric about the origin. since it's a function. it can't be symmetric about the x-axis.

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