\begin{frame} \frametitle{Representations of Functions} Functions can be represented in four ways: \begin{itemize} \pause \item verbally (a description in words)\vspace{-1ex} \begin{minipage}{.9\textwidth} \begin{exampleblock}{} Example: $A(r)$ is the area of a circle with radius $r$. \end{exampleblock} \end{minipage}\medskip \pause \item numerically (a table of values)\vspace{-1ex} \begin{minipage}{.9\textwidth} \begin{exampleblock}{} {\small \begin{tabular}{|l|l|l|l|} \hline $r$ & $1$ & $2$ & $3$\\ \hline $A(r)$ & $3.14159$ & $12.56637$ & $28.27433$\\ \hline \end{tabular} } \end{exampleblock} \end{minipage}\medskip \pause \item visually (a graph)\vspace{-1ex} \begin{minipage}{.9\textwidth} \begin{exampleblock}{} \begin{center} \scalebox{.5}{ \begin{tikzpicture}[default] \def\diax{r} \def\diay{A(r)} \diagram{-.5}{3}{-.5}{3}{1} \diagramannotatez \diagramannotatexx{1/1,2/2} \diagramannotateyy{1/10,2/20} \draw[cblue] plot[smooth,domain=0:3,samples=20] (\x,{.1*pi*\x^2}); \end{tikzpicture} } \end{center} \end{exampleblock} \end{minipage}\medskip \pause \item algebraically (an explicit formula)\vspace{-1ex} \begin{minipage}{.9\textwidth} \begin{exampleblock}{} $A(r) = \pi r^2$ \end{exampleblock} \end{minipage} \end{itemize} \end{frame}