\begin{frame} \frametitle{Polynomials of Degree 1: Linear Functions} \begin{block}{} A polynomial of degree $1$ is a \emph{linear function}:\vspace{-.5ex} \begin{talign} f(x) = mx + b \end{talign}\vspace{-3ex} \end{block} \begin{center} \scalebox{.6}{ \begin{tikzpicture}[default] \diagram{-2}{4}{-2}{4}{1} \diagramannotatez \diagramannotatex{-1,1,2,3} \diagramannotatey{-1,1,2,3} \draw[cblue,ultra thick] plot[smooth,domain=-2:4,samples=20] (\x,{.5*\x - 1}) node[right] {$f$}; \draw[cgreen,ultra thick] plot[smooth,domain=-1.5:1.5,samples=20] (\x,{2*\x +1}) node[right] {$g$}; \draw[cred,ultra thick] plot[smooth,domain=-2:4,samples=20] (\x,{-.25*\x +3}) node[right] {$h$}; \end{tikzpicture} } \end{center}\vspace{-1ex}\pause \begin{exampleblock}{} Find equations for the functions $f$, $g$ and $h$: \begin{itemize} \pause \item for $f$: \pause $f(x) = \frac{1}{2}x-1$ \item for $g$: \pause $f(x) = 2x+1$ \item for $h$: \pause $f(x) = -\frac{1}{4}x+3$ \end{itemize} \end{exampleblock} \end{frame}