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. For every odd-power term, replacing x with −x makes the term its opposite because (−x) raised to an odd power equals −x raised to that power. A constant term does not change, so it prevents the function from being odd.