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%\usepackage{opensans}          % Can't make this work so far. Shame. Would be lovely.
\usepackage[normalem]{ulem}     % For underlining links
% Most of the following are not required for the majority
% of cheat sheets but are needed for some symbol support.
\usepackage{amsmath}            % Symbols
\usepackage{MnSymbol}           % Symbols
\usepackage{wasysym}            % Symbols
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% Document Info
\author{maryfutbol}
\pdfinfo{
  /Title (algebra-final.pdf)
  /Creator (Cheatography)
  /Author (maryfutbol)
  /Subject (Algebra Final Cheat Sheet)
}

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% Header and Footer
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\fancyhead[L]{
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
    \SetRowColor{DarkBackground}
    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\end{tabulary}
\columnbreak
\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Algebra Final Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{maryfutbol} via \textcolor{DarkBackground}{\uline{cheatography.com/21780/cs/4286/}}}
\end{tabulary}
\end{multicols}}

\fancyfoot[L]{ \footnotesize
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
  \SetRowColor{FootBackground}
  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}maryfutbol \\
  \uline{cheatography.com/maryfutbol} \\
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 3rd June, 2015.\\
   Updated 12th May, 2016.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
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  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




\begin{document}
\raggedright
\raggedcolumns

% Set font size to small. Switch to any value
% from this page to resize cheat sheet text:
% www.emerson.emory.edu/services/latex/latex_169.html
\footnotesize % Small font.

\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Reciprocal Identities}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{csc x = 1/sin x \newline % Row Count 1 (+ 1)
sec x = 1/cos x \newline % Row Count 2 (+ 1)
cot x = 1/tan x% Row Count 3 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Half-angle identities}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{sin (x/2) = radical((1 - cos x) /2) \newline % Row Count 1 (+ 1)
cos (x/2) = radical((1 + cos x) / 2) \newline % Row Count 2 (+ 1)
tan (x/2) = (sin x / 1 + cos x)% Row Count 3 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Transformations}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Translations}} \newline % Row Count 1 (+ 1)
g(x) = f(x) + k is the graph of f(x) translated k units up when k \textgreater{} 0 and k units down when k \textless{} 0. \newline % Row Count 3 (+ 2)
g(x) = f(x − h) is the graph of f(x) translated h units right when h \textgreater{} 0 and h units left when h \textless{} 0. \newline % Row Count 6 (+ 3)
{\bf{Reflections}}	 \newline % Row Count 7 (+ 1)
g(x) = -f(x) is the graph of f(x) reflected in the x-axis. \newline % Row Count 9 (+ 2)
g(x) = f(-x) is the graph of f(x) reflected in the y-axis. \newline % Row Count 11 (+ 2)
{\bf{Dilations}}	 \newline % Row Count 12 (+ 1)
g(x) = a · f(x) is the graph of f(x) expanded vertically if a \textgreater{} 1 and compressed vertically if 0 \textless{} a \textless{} 1. \newline % Row Count 15 (+ 3)
g(x) = f(ax) is the graph of f(x) compressed horizontally if a \textgreater{} 1 and expanded horizontally if 0 \textless{} a \textless{} 1.% Row Count 18 (+ 3)
} \tn 
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Domain and range}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Domain}}: The domain of a function is the set of all possible input values (often the "x" variable), which produce a valid output from a particular function. It is the set of all real numbers for which a function is mathematically defined. \newline % Row Count 5 (+ 5)
{\bf{Range}}: The range is the set of all possible output values (usually the variable y, or sometimes expressed as f(x)), which result from using a particular function.% Row Count 9 (+ 4)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Cotangent/Tangent}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{tan x = sinx/cosx \newline % Row Count 1 (+ 1)
cot x = cosx/sinx% Row Count 2 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Double-angle identities}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{cos2x = cos\textasciicircum{}2\textasciicircum{}x - sin\textasciicircum{}2\textasciicircum{}x \newline % Row Count 1 (+ 1)
sin2x = (2sinx)(cosx) \newline % Row Count 2 (+ 1)
tan2x = (2tanx / 1 - tan\textasciicircum{}2\textasciicircum{}x)% Row Count 3 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Parent functions}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{constant function	 \newline % Row Count 1 (+ 1)
f(x) = a	graph is a horizontal line \newline % Row Count 2 (+ 1)
identity function	 \newline % Row Count 3 (+ 1)
f(x) = x	points on graph have coordinates (a, a) \newline % Row Count 4 (+ 1)
quadratic function	 \newline % Row Count 5 (+ 1)
f(x) = x\textasciicircum{}2\textasciicircum{}	graph is U-shaped \newline % Row Count 6 (+ 1)
cubic function	 \newline % Row Count 7 (+ 1)
f(x) = x\textasciicircum{}3\textasciicircum{}	graph is symmetric about the origin \newline % Row Count 8 (+ 1)
square root function		 \newline % Row Count 9 (+ 1)
f(x) = sqrt(x)  graph is in first quadrant \newline % Row Count 10 (+ 1)
reciprocal function		 \newline % Row Count 11 (+ 1)
f(x) = 1/x  graph has two branches \newline % Row Count 12 (+ 1)
absolute value function	 \newline % Row Count 13 (+ 1)
f(x) = │x│	graph is V-shaped% Row Count 14 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Pythagorean Identities}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{sin\textasciicircum{}2\textasciicircum{}x + cos\textasciicircum{}2\textasciicircum{}x = 1 \newline % Row Count 1 (+ 1)
tan\textasciicircum{}2\textasciicircum{}x + 1 = sec\textasciicircum{}2\textasciicircum{}x \newline % Row Count 2 (+ 1)
1 + cot\textasciicircum{}2\textasciicircum{}x = csc\textasciicircum{}2\textasciicircum{}x% Row Count 3 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{You can convert the first identity into the second and third by dividing both sides by cos\textasciicircum{}2\textasciicircum{}x or sin\textasciicircum{}2\textasciicircum{}x.}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Exponential and logarithmic}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Logarithmic \newline % Row Count 1 (+ 1)
y = ln x \newline % Row Count 2 (+ 1)
Exponential \newline % Row Count 3 (+ 1)
y = b\textasciicircum{}x\textasciicircum{}% Row Count 4 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}