\begin{frame} \frametitle{One-To-One Functions} \begin{exampleblock}{} How can we see from a graph if the function is one-to-one? \end{exampleblock} \medskip \begin{minipage}{.49\textwidth} \begin{center} \scalebox{.7}{ \begin{tikzpicture}[default,baseline=0cm] \diagram{-.5}{5}{-.5}{4}{1} \diagramannotatez \begin{scope}[ultra thick] \draw[cgreen,name path=curve] plot[smooth,domain=-.5:5,samples=300] (\x,{3+.3*\x-.3*pow((\x-2),2)}); \onslide<3->{ \draw[cred,dashed,name path=line] (-.5,3) -- (5,3); \path [name intersections={of = curve and line}]; \node[include=cred] at (intersection-1) {}; \node[include=cred] at (intersection-2) {}; \node at (2.25,-1.5) {not one-to-one}; } \end{scope} \end{tikzpicture} } \end{center} \end{minipage} \begin{minipage}{.49\textwidth} \begin{center} \scalebox{.7}{ \begin{tikzpicture}[default,baseline=0cm] \diagram{-.5}{5}{-.5}{4}{1} \diagramannotatez \begin{scope}[ultra thick] \draw[cgreen,name path=curve] plot[smooth,domain=0:4.1,samples=300] (\x,{2- .2*(\x-2) - .2*pow((\x-2),3)}); \onslide<4->{ \draw[cred,dashed,name path=line] (-.5,1.5) -- (5,1.5); \path [name intersections={of = curve and line}]; \node[include=cred] at (intersection-1) {}; \node at (2.25,-1.5) {one-to-one}; } \end{scope} \end{tikzpicture} } \end{center} \end{minipage} \pause\medskip \begin{block}{Horizontal Line Test} A function is one-to-one if and only if no horizontal line intersects its graph more than once. \end{block} \end{frame}