\begin{frame}
  \frametitle{Symmetry}
  
  
  \begin{exampleblock}{}
    Which of the following functions is even?
    \begin{enumerate}
      \item $f(x) = x^5 + x$
      \item $g(x) = 1 - x^4$
      \item $h(x) = 2x - x^2$
    \end{enumerate}
  \end{exampleblock}
  \pause\smallskip
  
  We have:
  \begin{enumerate}
  \pause
    \item $f(-x) = \pause (-x)^5 + (-x) =\pause -x^5 - x = \pause -(x^5+x) = \pause-f(x)$\\[.5ex]
       \pause Thus $f$ is odd.
  \pause
    \item $g(-x) = \pause 1 - (-x)^4 =\pause 1 - x^4 = \pause g(x)$\\[.5ex]
       \pause Thus $g$ is even.
  \pause
    \item $h(-x) = \pause 2(-x) - (-x)^2 =\pause -2x - x^2$\\[.5ex]
       \pause Thus $h$ is neither even nor odd.
  \end{enumerate}
  
  \pause\smallskip
  \begin{exampleblock}{}
    Note that:
    \begin{itemize}
      \item The sum of even functions is even (e.g. $1 + x^4$).
      \item The sum of odd functions is odd (e.g. $x^5 + x$).
    \end{itemize}
  \end{exampleblock}
  
\end{frame}