Finding Symmetries of a Function

[megacat8921]

How would one find the symmetry of the function x^3-3=g(x) ? Or any other symmetry.

 

[Ackbach]

I would replace $x$ with $-x$, and see what happens. Do you get the original back at you? Then it's even. Do you get the negative? Then it's odd.

 

[Greg]

Graphing is another method. For example, graphing $$y=(x-3)^2$$ makes it easy to see the function is symmetrical about the line $x=3$.

 

[samir]

I would replace $x$ with $-x$, and see what happens. Do you get the original back at you? Then it's even. Do you get the negative? Then it's odd.

Graphing is another method. For example, graphing $$y=(x-3)^2$$ makes it easy to see the function is symmetrical about the line $x=3$.

Can we say that all cubic functions are always symmetrical at a single point, and never along a line?