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\title{Functions, Limits, Derivatives}
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\author{}
\institute{\large \textbf{Learning Outcomes}:\\[6pt] Identify properties of elementary fuctions (formed by composition of power, exponential, logarithmic, and trigonomtric functions and their inverses)}
\date{}
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\begin{document}
\metroset{block=fill}
\begin{frame}
\titlepage
\end{frame}
\begin{frame}[t]{Functions}\vspace{4pt}
\begin{block}{Definition of a Function}
\vspace{0.5em}
A \textbf{function} $f$ is a rule that assigns to each element $x$ in a set $D$ exactly one element, called $f(x)$, in a set $E$.
\vspace{0.5em}
\end{block}
\vspace{10pt}
Set $D$ is called the
\only<1>{\line(1,0){40}}
\only<2>{\textcolor{magenta}{domain}}
\,of the function.\\[10pt]
Set $E$ is called the
\only<1>{\line(1,0){40}}
\only<2>{\textcolor{magenta}{range}}
\,of the function.
\end{frame}
\begin{frame}{Your Very First Flash Card}
\begin{columns}[onlytextwidth]
\column{0.5\textwidth}
$\sqrt{x^2} = $\\[10pt]
\begin{enumerate}[(A)]
\item $x$
\item $-x$
\item $|x|$
\item undefined
\end{enumerate}
\column{0.5\textwidth}
\only<3>{
$\sqrt{x^2}=
\begin{cases}
-x, & x<0 \\
x, & x \geq 0
\end{cases}$\\[10pt]}
\only<2->{
\begin{tikzpicture}[scale=0.6]
\begin{axis}[xlabel = {$x$}, ylabel={$\sqrt{x^2}$},
,axis lines=middle
,samples=100, grid, thick
,xmin=-6, xmax=6, ymin=-6, ymax=6]
\addplot[blue, ultra thick] {(x^2)^0.5};
\end{axis}
\end{tikzpicture}
}
\end{columns}
\end{frame}
\begin{frame}[t]{Parent Fucntion}\vspace{4pt}
You should be able to identify by name and sketch a graph of each of the following parent functions
\begin{enumerate}
\begin{multicols}{3}
\item $y=x$
\item $y=|x|$
\item $y=x^2$
\item $y=x^3$
\item $y=x^b$
\onslide<2->{
\item $y=\sqrt{x}$
\item $y= \sqrt[3]{x}$
\item $y=\frac{1}{x}$
\item $y=2^x$
\item $y=e^x$
}
\onslide<3->{
\item $y=\ln x$
\item $y=\frac{1}{1+e^{-x}}$
\item $y=\sin x$
\item $y=\cos x$
\item $y=\tan x$}
\end{multicols}
\end{enumerate}
\end{frame}
\begin{frame}{standout}
\flushleft
Homework: p.342\#7-21
\end{frame}
\end{document}