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\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}