Is it possible for a function to be symmetrical and yet neither even or odd? Explain.

Question

symmetrical and neither even or odd?

Answer 1

odd and even functions are symmetrical with respect to the y axis or with respect to the orgin

 

f(-x) = f(x) is symmetrical to the y axis and is an even function; example f(x) = x^2

 

f(-x) = f(x) is symmetrical to the orgin and is an odd function; example f(x) = x^3

 

 

Now consider the shifted functions f(x) = (x-2)^2 and f(x) = x^3 - 2 which are neither even nor odd functions.