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\begin{frame}
  \frametitle{Power Functions: Special Cases}
  
  \begin{exampleblock}{}
  We consider $x^{\frac{1}{n}}$ where $n$ is a positive integer:
  \begin{itemize}
    \item $f(x) = x^{\frac{1}{n}} = \sqrt[n]{x}$ is a \emph{root function} (square root for $n=2$)
  \end{itemize}
  \end{exampleblock}
  \medskip
  
  \begin{minipage}{.49\textwidth}
  \scalebox{.8}{
  \begin{tikzpicture}[default,baseline=0ex]
    \diagram{-1}{3}{-2}{2}{1}
    \diagramannotatez
    \diagramannotatex{-1,1}
    \diagramannotatey{-1,1}
    \begin{scope}[ultra thick]
    \draw[cgreen] plot[smooth,domain=0.00001:3,samples=100] (\x,{pow(\x,1/6)});
    \draw[cred] plot[smooth,domain=0.00001:3,samples=100] (\x,{pow(\x,1/4)});
    \draw[cblue] plot[smooth,domain=0.00001:3,samples=100] (\x,{pow(\x,1/2)});
    
    \draw[cblue] (-1.1cm,-2.8cm) -- node [at end,right] {$x^{\frac{1}{2}}$} +(.8cm,0);
    \draw[cred] (0.4cm,-2.8cm) -- node [at end,right] {$x^{\frac{1}{4}}$} +(.8cm,0);
    \draw[cgreen] (1.9cm,-2.8cm) -- node [at end,right] {$x^{\frac{1}{6}}$} +(.8cm,0);
    
    \node (a) [include=black,minimum size=1mm] at (1,1) {};
    \node[r=(a),yshift=-2mm] {$(1,1)$};
    \end{scope}
  \end{tikzpicture}
  }
  \end{minipage}
  \begin{minipage}{.49\textwidth}
  \scalebox{.8}{
  \begin{tikzpicture}[default,baseline=1cm]
    \diagram{-2}{2}{-2}{2}{1}
    \diagramannotatez
    \diagramannotatex{-1,1}
    \diagramannotatey{-1,1}
    \begin{scope}[ultra thick]
    \draw[cgreen] plot[smooth,domain=0.00001:2,samples=100] (\x,{pow(\x,1/7)});
    \draw[cgreen] plot[smooth,domain=-2:-0.00001,samples=100] (\x,{-pow(-\x,1/7)});
    \draw[cred] plot[smooth,domain=0.00001:2,samples=100] (\x,{pow(\x,1/5)});
    \draw[cred] plot[smooth,domain=-2:-0.00001,samples=100] (\x,{-pow(-\x,1/5)});
    \draw[cblue] plot[smooth,domain=0.00001:2,samples=100] (\x,{pow(\x,1/3)});
    \draw[cblue] plot[smooth,domain=-2:-0.00001,samples=100] (\x,{-pow(-\x,1/3)});
    
    \draw[cblue] (-2.1cm,-2.8cm) -- node [at end,right] {$x^{\frac{1}{3}}$} +(.8cm,0);
    \draw[cred] (-.6cm,-2.8cm) -- node [at end,right] {$x^{\frac{1}{5}}$} +(.8cm,0);
    \draw[cgreen] (.9cm,-2.8cm) -- node [at end,right] {$x^{\frac{1}{7}}$} +(.8cm,0);

    \node (a) [include=black,minimum size=1mm] at (1,1) {};
    \node[r=(a),yshift=-2mm] {$(1,1)$};
    \node (b) [include=black,minimum size=1mm] at (-1,-1) {};
    \node[l=(b),yshift=2mm] {$(-1,-1)$};
    \end{scope}
  \end{tikzpicture}
  }
  \end{minipage}
  \pause\medskip
  
  \begin{itemize}
    \item For even $n$ the domain is $[0,\infty)$,
          the graph is similar to $\sqrt{x}$.
    \item For odd $n$ the domain is $\mathbb{R}$,
          the graph is similar to $\sqrt[3]{x}$.
  \end{itemize}
  \vspace{10cm}
\end{frame}