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 $\displaystyle \neq$ -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 ?