\begin{frame} \frametitle{Exponential Functions: Three Types} \begin{center} \begin{minipage}{.45\textwidth} \scalebox{.6}{ \begin{tikzpicture}[default,baseline=0cm,scale=1.2,nodes={scale=.9}] {\diagram{-2.5}{2.5}{-.5}{3}{1}} \diagramannotatez \diagramannotatey{1} \begin{scope}[ultra thick] \draw[cblue] plot[smooth,domain=-1.6:2.5,samples=300] (\x,{.5^\x}); \end{scope} \end{tikzpicture} }\\[.5ex] \centerline{{\small $f(x) = a^x$ with $0 < a < 1$}} \end{minipage} \begin{minipage}{.45\textwidth} \scalebox{.6}{ \begin{tikzpicture}[default,baseline=0cm,scale=1.2,nodes={scale=.9}] {\diagram{-2.5}{2.5}{-.5}{3}{1}} \diagramannotatez \diagramannotatey{1} \begin{scope}[ultra thick] \draw[cgreen] plot[smooth,domain=-2.5:1.6,samples=300] (\x,{2^\x}); \end{scope} \end{tikzpicture} }\\[.5ex] \centerline{{\small $f(x) = a^x$ with $a > 1$}} \end{minipage} \bigskip \begin{minipage}{.45\textwidth} \scalebox{.6}{ \begin{tikzpicture}[default,baseline=0cm,scale=1.2,nodes={scale=.9}] {\diagram{-2.5}{2.5}{-.5}{3}{1}} \diagramannotatez \diagramannotatey{1} \begin{scope}[ultra thick] \draw[orange] plot[smooth,domain=-2.5:2.5,samples=300] (\x,{1^\x}) node [right] {$1^x$}; \end{scope} \end{tikzpicture} }\\[.5ex] \centerline{{\small $f(x) = 1^x$}} \end{minipage} \begin{minipage}{.50\textwidth} \begin{itemize} \pause \item constant for $a = 1$ \pause \item increasing for $a > 1$ \pause \item decreasing for $0 < a < 1$ \pause \item domain = $(-\infty,\infty)$ \pause \item range = $(0,\infty)$ if $a\ne 1$ \end{itemize} \end{minipage} \end{center} \end{frame}