translations.tex

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\title[BT] % (optional, only for long titles)
{\textcolor{blue-violet}{\textbf{Taking derivatives to the \nth}} \\  \vspace{0.1in}   \textcolor{black}{Minisymposium} \\  \textcolor{black}{University of Nebraska at Kearney}}

\author[BW] % (optional, for multiple authors)
{Barton~Willis}
\institute[UNK] % (optional)
{
 % \inst{1}%
     Professor and Chair \\
     Department of Mathematics and Statistics\\
     {College of Arts and Sciences} \\
    University Nebraska at Kearney  \\
    Kearney, Nebraska 68849,  USA \\
   \href{mailto:willisb@unk.edu}{willisb@unk.edu} \\
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\begin{frame}\textcolor{blue-violet}{\Large Four simple rules (for translations)}

\vspace{0.1in}

Let \(E\) be any equation in the variables \(x\)  (horizontal) and \(y\)  (vertical). Let \(h,k\), and \(a\) be real numbers
with $a$ positive.
\vspace{0.1in}
\begin{PenList}

\item  \(x \to x - h\) shifts the graph of \(E\) \emph{h units to the  right}.
\vspace{0.1in}
\item  \(y \to x - k\) shifts the graph of \(E\) \emph{k units up}.
\vspace{0.1in}
\item \(x \to x/a\) horizontally stretches the graph of \(E\) \emph{by a factor of a}.
\vspace{0.1in}
\item  \(y \to y/a\) vertically  stretches the graph of \(E\) \emph{by a factor of a}.

\vspace{0.1in}

\item It doesn't matter if the equation is solved for \(y\). 
\vspace{0.1in}

\item \(-h\)  units right is the same as \(h\) units left; \(-k\)  units up  is the same as \(k\) units down.  
\vspace{0.1in}

\item A stretch of a factor of \(a\) is the same as squeeze by a factor of \(1/a\).

\vspace{0.1in}

\item Oops, that's seven rules (but four of them are simple).

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