\begin{frame} \frametitle{Algebraic Functions: Real-wold Example} \begin{exampleblock}{} The following algebraic function occurs in the theory of relativity. The mass of an object with velocity $v$ is: \begin{talign} m = f(v) = \frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}} \end{talign} where \begin{itemize} \item $m_0$ is the rest mass of the object \item $c \approx 3.0 \cdot 10^5 \frac{\text{km}}{\text{h}}$ is the speed of light (in vacuum) \end{itemize} \end{exampleblock} \begin{center} \scalebox{.7}{ \begin{tikzpicture}[default,baseline=1cm] {\def\diaborderx{.9cm} \def\diabordery{.7cm} \def\diax{v} \def\diay{m} \diagram{0}{4}{0}{4}{1}} \diagramannotatez \diagramannotatexx{1/$\frac{1}{3}c$,2/$\frac{2}{3}c$} \diagramannotateyy{1/$m_0$,2/$2m_0$} \begin{scope}[ultra thick] \draw[cblue] plot[smooth,domain=0:2.91,samples=290] (\x,{1/(sqrt(1-pow(\x/3,2)))}); \end{scope} \draw[cred,dashed] (3,4) -- node[at end,below] {$c$} (3,-.2); \end{tikzpicture} }\\\smallskip \end{center} \end{frame}