Linear functions/translation of graphs

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SUMMARY

The discussion focuses on analyzing the cubic function f(x) = x^3 - 3x, specifically regarding its critical points and symmetry properties. The function is factored as f(x) = x(x^2 - 3), which reveals the roots at x = 0, x = √3, and x = -√3. The symmetry is examined through the conditions f(-x) = f(x) for even symmetry and f(-x) = -f(x) for odd symmetry, confirming that this function is odd.

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The question is

Graph f(x)=X^3-3x. Does it have any high or low points? What about symmetry?

Okay the problem I'm having is what formula to use with a ^3 on the X, my previous 2 problems I did by using the quad formula, those questions were f(x)= 2x^4+4x^2-1, and f(x)= 16x^2+4x-3 respectively.
 
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f(x)= x^3- 3x= x(x^2- 3). What values of x makes f(x)= 0? What happens between those values of x?
 
What about symmetry?

f(x) = f(-x)?

f(-x) = -f(x)?
 

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