SOLUTION: How do I determine if the following polynomial functions have even or odd symmetry, or neither/ how do I justify my reasoning? A) f(x)=-x^3 +3x B) f(x)=x^4+x^2+x C) f(x)=x^

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: How do I determine if the following polynomial functions have even or odd symmetry, or neither/ how do I justify my reasoning? A) f(x)=-x^3 +3x B) f(x)=x^4+x^2+x C) f(x)=x^      Log On


   

Question 1119949: How do I determine if the following polynomial functions have even or odd symmetry, or neither/ how do I justify my reasoning?
A) f(x)=-x^3 +3x
B) f(x)=x^4+x^2+x
C) f(x)=x^6-x^4-x^2
D) f(x)+1/3x^4-2/3x^2
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
change the sign of x and look at the polynomial
A: (-x)^3-3x=-x^3-3x, which is -(x^3+3x), so that is f(-x)=-f(x) or odd.
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E3%2B3x%2C-x%5E3-3x%29
B: This becomes x^4+x^2-x which is neither even nor odd.
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E4%2Bx%5E2%2Bx%2Cx%5E4%2Bx%5E2-x%29
C:This becomes x^6+x^4+x^2, which is the same, so even.
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E6%2Bx%5E4%2Bx%5E2%29
D:This becomes 1(3x^4)-2/(3x^2), which is also the same, so even.
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C%281%2F3x%5E4%29-%282%2F3x%5E2%29%29