[tex]\bf y=x^3-4x
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\textit{check for y-axis symmetry}\\\\
\stackrel{x=-x}{y=(-x)^3-4(-x)}\implies y=(-x)(-x)(-x)+4x\implies \boxed{y=-x^3+4x}
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\textit{checking for x-axis symmetry}\\\\
\stackrel{y=-y}{(-y)=x^3-4x}\implies -y=x^3-4x\implies \boxed{y=-x^3+4x}
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\textit{checking for origin symmetry}\\\\
\stackrel{x=-x\qquad y=-y}{(-y)=(-x)^3-4(-x)}\implies -y=(-x)(-x)(-x)+4x
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-y=-x^3+4x\implies y=\cfrac{-x^3+4x}{-1}\implies \boxed{y=x^3-4x}\quad \checkmark[/tex]
notice, if you replace x = -x and y = -y accordingly for each test for symmetry, if the resulting function, is equal to the original function, then it has that type of symmetry.
