SOLUTION: please help me using algebraic test to check for symmetry with both x and origin. X to the power 4 minus X-squared plus 3.thanx

Question 948698: please help me using algebraic test to check for symmetry with both x and origin. X to the power 4 minus X-squared plus 3.thanx
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
please help me using algebraic test to check for symmetry with both x and origin. X to the power 4 minus X-squared plus 3.please help me using algebraic test to check for symmetry with both x and origin. X to the power 4 minus X-squared plus 3.
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The Rules::
y-axis symmetry if f(x) = f(-x)
origin symmetry if f(x) = -f(-x)
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f(x) = x^40 - x^2 + 3
f(-x) = (-x)^40 - (-x)^2 + 3 = x^40 - x^2 + 3
-f(-x) = -x^40 + x^2 - 3
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Conclusion::
Since f(x)=f(-x) f has y-axis symmetry.
Since f(x) does not equal -f(-x) f does not have origin symmetry.
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Cheers,
Stan H.
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