Dimetri says that a function that is made of terms where the variable is raised only to an odd power will be an odd function. Do you agree with Dimetri? Explain why or why not.

Answer:

Dimetri is correct only if there is no constant term. Replacing x with −x changes the sign of every term with an odd power, but it does not change a constant. Therefore, the function is odd only when there is no constant term.