Can an Odd Polynomial ever have a Line of Symmetry?

Question

Focusing on the key features of polynomials, Can an Odd Polynomial ever have a Line of Symmetry? Please explain your answer.

Answer 1

f(x) = cosx is an even function with line of symmetry x=0 or x=2npi where n= any integer, cosx= cos(-x)

f(x) = sinx is an odd function with line of symmetry x=pi/2 or x=pi/2 + 2npi where n = any integer sinx =-sin(-x)

y= f(x) = absolute value of x has line of symmetry x=0, f(x)=f(-x)

f(x) = y= x has line of symmetry y=-x, f(x)=-f(-x) or -f(x)=f(-x) is symmetric about the origin

Answer 2

y=x has line of symmetry of itself.