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\setbeamertemplate{frame numbering}[fraction]
\setbeamercolor{background caanvas}{bg=white}

% \usetheme{Warsaw}

\title{Functions, Limits, Derivatives}
% \subtitle{Subtitle Here}
\institute{\large \textbf{Learning Outcomes}:\\[6pt] Identify properties of elementary fuctions (formed by composition of power, exponential, logarithmic, and trigonomtric functions and their inverses)}



\begin{block}{Definition of a Function}
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 $E$.

Set $D$ is called the 
\,of the function.\\[10pt]
Set $E$ is called the 
\,of the function.


\begin{frame}{Your Very First Flash Card}
$\sqrt{x^2} = $\\[10pt]
\item $x$
\item $-x$
\item $|x|$
\item undefined
-x, & x<0 \\
x, & x \geq 0

\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};


\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
    \item $y=x$
    \item $y=|x|$
    \item $y=x^2$
    \item $y=x^3$
    \item $y=x^b$
    \item $y=\sqrt{x}$
    \item $y= \sqrt[3]{x}$
    \item $y=\frac{1}{x}$
    \item $y=2^x$
    \item $y=e^x$
    \item $y=\ln x$
    \item $y=\frac{1}{1+e^{-x}}$
    \item $y=\sin x$
    \item $y=\cos x$
    \item $y=\tan x$}

Homework: p.342\#7-21