How do you determine if #-x^3 + 6x# is an even or odd function?

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Answer 1 · 2017-01-05T10:25:28

This is an odd function

Let #f(x)=-x^3+6x#

Then,

#f(-x)=-(-x)^3+6(-x)=x^3-6x#

#-f(x)=-(-x^3+6x)=x^3-6x=f(-x)#

This is an odd function as #f(-x)=-f(x)#

An even function is #f(x)=f(-x)#

An odd function is symmetric wrt the origin #O#

graph{-x^3+6x [-18.03, 18.02, -9.01, 9.02]}