\begin{frame} \frametitle{Vertical Line Test} When does a curve represent a function? \onslide<2->{ \begin{block}{Vertical Line Test} A curve in the $xy$-plane represents a function of $x$ if and only if no vertical line intersects the curve more than once. \end{block} } \begin{center} \scalebox{.6}{ \begin{tikzpicture}[default] \diagram{-.5}{5.5}{-.5}{5.5}{1} \diagramannotatez \draw[cblue,ultra thick,name path=curve] (0,1) to[in=180] (2,3) to[out=0,in=180] (4,2) to[out=0,in=-120] (5,3); \onslide<2->{ \draw[cred,dashed,name path=line] (4,-.2) -- node[at start,below] {$a$} (4,5); \path [name intersections={of = curve and line}]; \node[include=cred] at (intersection-1) {}; \node at (2.5,-1.5) {corresponds to a function of $x$}; } \end{tikzpicture} }\hspace{1cm} \scalebox{.6}{ \begin{tikzpicture}[default] \diagram{-.5}{5.5}{-.5}{5.5}{1} \diagramannotatez \draw[cblue,ultra thick,name path=curve] (0,1) to[in=180] (2,3) to[out=0,in=180] (4,2) to[out=0,in=30,looseness=2] (3,4); \onslide<2->{ \draw[cred,dashed,name path=line] (4,-.2) -- node[at start,below] {$a$} (4,5); \path [name intersections={of = curve and line}]; \node[include=cred] at (intersection-1) {}; \node[include=cred] at (intersection-2) {}; \node at (2.5,-1.5) {does not correspond to a function of $x$}; } \end{tikzpicture} } \end{center} \vspace{-1ex} \end{frame}