dimetri says that a function that is made of terms where the variable is raised only to an odd power will be…

Brief Explanations:

An odd - function is defined as (f(-x)=-f(x)) for all (x) in the domain. If a function (f(x)) is composed of terms like (a_nx^{2n + 1}) (where (n) is a non - negative integer and (a_n) is a constant), then (f(-x)=a_n(-x)^{2n + 1}=-a_nx^{2n+1}). Summing up such terms for a function will still satisfy (f(-x)=-f(x)).

Answer:

Yes, I agree with Dimetri. A function made of terms where the variable is raised only to an odd power will be an odd function because for each term (ax^k) with (k) odd, (a(-x)^k=-ax^k), and when we consider the whole function as a sum of such terms, (f(-x)=-f(x)) holds.