Question

How Do I test this equation `y=x^3-3x` for the x-axis, y-axis or origin symmetry?

Answer 1

`x-"axis":f(x)=-f(x)`
`y-"axis":f(x)=f(-x)`
`"origin":-f(x)=f(-x)`

`f(-x)=(-x)^3-3(-x)=-x^3+3x`

`-f(x)=-(x^3-3x)=-x^3+3x`

`-f(x)=f(-x)`, equation has origin symmetry.
graph{x^3-3x [-10, 10, -5, 5]}