\begin{frame} \frametitle{Visualizing Functions as Graphs} \begin{block}{} The \emph{graph} of a function $f$ is the set of pairs \;$\{\;(x,f(x)) \mid x \in D\;\}$ \end{block} \begin{itemize} \item<2-> set of all points $(x,y)$ in the coordinate plane\\ such that $y = f(x)$ and $x$ is in the domain \end{itemize} \begin{center} \scalebox{.7}{ \begin{tikzpicture}[default] \diagram{-1}{5}{-1}{5}{1} \diagramannotate \begin{scope}[cdblue,ultra thick] \draw (-1cm,1cm) to[in=180] (0,1.5cm) to[out=0,in=180] (1cm,1cm) to[out=0,in=-135,looseness=.5] (3cm,4cm) to[out=45,in=135] (5cm,2cm); \end{scope} \begin{scope} \draw [cdred,dashed] (1cm,1cm) -- (1cm,0cm); \draw [decorate,decoration={brace,amplitude=2mm},xshift=1mm] (1cm,.9cm) -- node [right,xshift=2mm] {$f(1)$} (1cm,0.1cm); \draw [cdred,dashed] (3cm,4cm) -- (3cm,0cm); \draw [decorate,decoration={brace,amplitude=2mm},xshift=1mm] (3cm,3.9cm) -- node [right,xshift=2mm] {$f(x)$} (3cm,0.1cm); \node (x) [anchor=north] at (3cm,0cm) {$x$}; \node (p) [cdblue,inner sep=0] at (3cm,4cm) {$\bullet$}; \node [at=(p.north west),anchor=south east,inner sep=0] {$(x,f(x))$}; \end{scope} \end{tikzpicture} }\pause\pause\quad\nolinebreak \scalebox{.7}{% \begin{tikzpicture}[default] \diagram{-1.5}{5}{-1}{5}{0} \begin{scope}[cdblue,ultra thick] \draw (1cm,1.5cm) to[in=180] (3cm,3.5cm) to[out=0,in=120] (4cm,2.5cm); \node [cdblue] (start) at (1cm,1.5cm) {$\bullet$}; \node [cdblue] (end) at (4cm,2.5cm) {$\bullet$}; \node [cdblue] (high) at (3cm,3.5cm) {}; \node [clblue] (d1) at (1cm,0cm) {$\bullet$}; \node [clblue] (d2) at (4cm,0cm) {$\bullet$}; \node [clblue] (r1) at (0cm,1.5cm) {$\bullet$}; \node [clblue] (r2) at (0cm,3.5cm) {$\bullet$}; \begin{scope}[dashed,thick] \draw (r1) -- (start); \draw (r2) -- (high); \draw (d1) -- (start); \draw (d2) -- (end); \end{scope} \begin{scope}[black] \draw [decorate,decoration={brace,amplitude=2mm},xshift=-3mm] (r1.west) -- node [left,xshift=-3mm] {range} (r2.west); \draw [decorate,decoration={brace,amplitude=2mm},xshift=3mm] (d2.south) -- node [below,yshift=-3mm] {domain} (d1.south); \end{scope} \end{scope} \begin{scope} \end{scope} \end{tikzpicture} } \end{center} \end{frame}