Entry 6446

% -----------------------------------------------------------
% AMS-LaTeX for highlighting
% -----------------------------------------------------------
\documentclass[12pt]{article}
\usepackage{amsmath,amsthm,amsfonts,eucal,amssymb}
\usepackage{ifpdf}
%
\usepackage{graphicx,color}
%\usepackage{fancyhdr}
%\usepackage{graphpap}
%\usepackage{oletex}
%\usepackage{layout}
%
% PDF Output
%
\ifpdf
\usepackage[pdftex]{hyperref}
\hypersetup{%
pdftitle = {Function Transformation Summary},
pdfsubject = {Summary table of the effect of simple transformations on the graph of a function},
pdfkeywords = {function transformation},
pdfauthor = {},
pdfcreator = {\LaTeX\ with package \flqq hyperref\frqq},
pdfproducer = {pdfTeX-0.\the\pdftexversion\pdftexrevision},
colorlinks = {true},
linkcolor  = {red},
urlcolor = {blue},
}
\pdfinfo{/CreationDate (D:20100823000000-01'00')}
\else
\usepackage{hyperref}
\fi

% Fancy Header Set Up

%\pagestyle{fancy} \lfoot{}\cfoot{}\rfoot{}%
%\lhead{August 16, 2006}
%\chead{\bfseries Transformations of Functions}%
%\rhead{\thepage}

\newlength{\myw}
\setlength{\myw}{1in}

% ----------------------------------------------------------------
\vfuzz3pt % Don't report over-full v-boxes if over-edge is small
\hfuzz2pt % Don't report over-full h-boxes if over-edge is small
% ----------------------------------------------------------------
\begin{document}
\thispagestyle{empty}
%
\begin{center}
\bfseries %
Transformations of Functions
\end{center}
% ----------------------------------------------------------------
%
\begin{center}
%
\renewcommand{\arraystretch}{1.25}
%
\begin{tabular}{||p{1.1in}|p{4in}||}
\hline\hline The graph of: & is the graph of $y=f(x)$:\\
\hline\hline
%
$\displaystyle f(x) + k$ & %
shifted up vertically $k$ units; \\
%
\hline
%
$\displaystyle af(x)\quad (a>0)$ & %
stretched or contracted vertically by a factor of $a$; \\
%
\hline
%
$\displaystyle -f(x)$ & %
reflected in the $x$-axis; \\
%
\hline
%
$\displaystyle |f(x)|$ & %
with those parts of the graph below the $x$-axis reflected above it; \\
%
\hline
%
$\displaystyle f(x-h)$ & %
shifted right horizontally $h$ units; \\
%
\hline
%
$\displaystyle f(bx)\quad (b>0)$ & %
stretched or contracted horizontally by a factor of $1/b$; \\
%
\hline
%
$\displaystyle f(-x)$ & %
reflected in the $y$-axis; \\
%
\hline
%
$\displaystyle f(|x|)$ & %
with the part to the left of the $y$-axis replaced by a reflection of the part to the right; \\
%
\hline
%
\parbox{\myw}{The inverse function of $f$}\rule{0ex}{4ex} & %
reflected in the diagonal line $y=x$. \\
\hline
%
\hline
%
\end{tabular}
%
\end{center}
%
\textbf{Be careful of the order in which you apply the transformations.
Both the  new function and its graph depend on the order in which
the transformations are applied.
}% ----------------------------------------------------------------
\end{document}
% ----------------------------------------------------------------