\begin{frame} \frametitle{Functions} \begin{example} The area $A$ of a circle depends on its radius $r$. The rule is $$A = \pi r^2$$ We say that $A$ is a \emph{function} of $r$. \end{example} \bigskip \begin{minipage}{.49\textwidth} \begin{center} \begin{tikzpicture}[default,nodes={scale=.8,inner sep=1mm}] \draw[fill=cblue!10] (0,0) circle (1.5cm); \node[cblue] at (0,-.75cm) {area $A = \pi r^2$}; \draw[cred,dotted] (0,0) -- node[above] {radius $r$} (1.5cm,0mm); \draw[fill=black] (0,0) circle (.5mm); \end{tikzpicture} \end{center} \end{minipage} \pause \begin{minipage}{.49\textwidth} \begin{center} \scalebox{.7}{ \begin{tikzpicture}[default] \def\diax{r} \def\diay{A} \diagram{-1}{4}{-1}{4}{1} \diagramannotatez \diagramannotatexx{1/1 cm,2/2 cm,3/3 cm} \diagramannotateyy{1/10 cm$^2$,2/20 cm$^2$,3/30 cm$^2$} \draw[cblue] plot[smooth,domain=0:3.6,samples=20] (\x,{.1*pi*\x^2}); \end{tikzpicture} } \end{center} \end{minipage} \end{frame}