\begin{frame}
  \frametitle{One-To-One Functions}
  
  \begin{block}{}
    A \emph{one-to-one function} is a function that never takes
    the same value twice, that is:
    \begin{talign}
      f(x) \ne f(y) \quad \text{ whenever $x \ne y$}
    \end{talign}
  \end{block}
  \pause\medskip
  
  \begin{minipage}{.50\textwidth}
  \begin{center}
    \begin{tikzpicture}[default]
      \draw [fill=cblue!20,draw=cdblue] (0cm,0cm) to[out=10,in=90] (1cm,-1cm) to[out=-90,in=-10] (0cm,-2cm) to[out=170,in=-90,looseness=1.5] (-.2cm,-1cm) to[out=90,in=190,looseness=1.5] (0,0);
      \node (D) at (0,-2.6cm) {$D$};
      \node (x) at (.2cm,-.4cm) {$a$}; 
      \node (a) at (.4cm,-1cm) {$b$}; 
      \node (z) at (.1cm,-1.7cm) {$z$}; 
      \begin{scope}[xshift=35mm]
      \draw [fill=cblue!20,draw=cdblue,rotate=-20] (0cm,-1cm) ellipse (1cm and 1.3cm);
      \node (E) at (-.5,-2.6cm) {$E$};
      \node (a') at (-.2cm,-.1cm) {$a$}; 
      \node (c') at (-.4cm,-.8cm) {$b$}; 
      \node (q') at (-.5cm,-1.7cm) {$d$}; 
      \node (p') at (-0cm,-1.2cm) {$c$}; 
      \end{scope}
      \begin{scope}[cdred,->,>=stealth,thick]
      \draw (x) to[bend left=20] (a');
      \draw (a) to[bend left=-10] (a');
      \draw (z) to[bend left=-20] (q');
      \draw [shorten >= 5mm, shorten <= 5mm] (D) to node [above,black] {$f$} (E);
      \end{scope}
    \end{tikzpicture}
  \end{center}
  \end{minipage}
  \begin{minipage}{.49\textwidth}
  \begin{center}
    \begin{tikzpicture}[default]
      \draw [fill=cblue!20,draw=cdblue] (0cm,0cm) to[out=10,in=90] (1cm,-1cm) to[out=-90,in=-10] (0cm,-2cm) to[out=170,in=-90,looseness=1.5] (-.2cm,-1cm) to[out=90,in=190,looseness=1.5] (0,0);
      \node (D) at (0,-2.6cm) {$D$};
      \node (x) at (.2cm,-.4cm) {$a$}; 
      \node (a) at (.4cm,-1cm) {$b$}; 
      \node (z) at (.1cm,-1.7cm) {$z$}; 
      \begin{scope}[xshift=35mm]
      \draw [fill=cblue!20,draw=cdblue,rotate=-20] (0cm,-1cm) ellipse (1cm and 1.3cm);
      \node (E) at (-.5,-2.6cm) {$E$};
      \node (a') at (-.2cm,-.1cm) {$a$}; 
      \node (c') at (-.4cm,-.8cm) {$b$}; 
      \node (q') at (-.5cm,-1.7cm) {$d$}; 
      \node (p') at (-0cm,-1.2cm) {$c$}; 
      \end{scope}
      \begin{scope}[cdred,->,>=stealth,thick]
      \draw (x) to[bend left=20] (a');
      \draw (a) to[bend left=-10] (q');
      \draw (z) to[bend left=-20] (c');
      \draw [shorten >= 5mm, shorten <= 5mm] (D) to node [above,black] {$g$} (E);
      \end{scope}
    \end{tikzpicture}
  \end{center}
  \end{minipage}
  \pause\medskip
  
  \begin{exampleblock}{}
    Which of these function is one-to-one?
    \pause The function $g$.
  \end{exampleblock}
\end{frame}