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How to test for symmetry?? Test the equation for symmetry and sketch its graph. x=square root of y

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Okay, thanks for the graph. but how do you test for symmetry?
Substitute Symmetry across the y-axis: see of f(x) = f(-x) Symmetry across the x-axis: see of f(y) = f(-y) Symmetry across the origin: see of f(x) = -f(-x)

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I don't understand can you like show me an exapmle
y = x^2 Substitute -x y = (-x)^2 = (-1)^2 * (x^2) = x^2 EXACTLY the same. Symmetry about the y-axis.
what about the x azis?
functions dont have a test about the x axis since a function only defines a unique value for any given x
there are tests for about the y axis, about the origin, and if its a "relation" then we can try tests for about the x axis a spose; see if -y and y can stem from the same x value
then how to test about the origin?
if you negate the input, does it produce a negated output?

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