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Math Help - Odd Polynomial Functions

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    Odd Polynomial Functions

    Prove algebraically and explain grahically why a polynomial that is an odd function is no longer an odd function when a non-zero constant is added. Provide examples.

    Thanks in advance :P
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    Quote Originally Posted by ahling View Post
    Prove algebraically and explain grahically why a polynomial that is an odd function is no longer an odd function when a non-zero constant is added. Provide examples.

    Thanks in advance :P
    If a polynomial P is an odd function, then P(-x)=-P(x).

    So if you add a constant, say m, then let Q(x)=P(x)+m.
    The thing is now to prove that Q is not odd.

    Q(-x)=P(-x)+m=-P(x)+m \neq -Q(x)=-(P(x)+m)

    Do you quite understand ?


    Graphically, adding a constant means to level up (or down) the curve. Will it still be symmetric wrt the center of the graph ?
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