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\begin{document}
\begin{center}

{\Huge{Precalculus Review}}\\
\end{center}



\noindent Consider the maps defined below for this worksheet:

\begin{tabular*}{6.0in}{l@{\extracolsep{\fill}}l}
$f:\mathbb{R}\rightarrow \mathbb{R}$		&$g:\mathbb{R}\setminus \{1\}\rightarrow \mathbb{R}$\\
$x \mapsto (x-2)^2$						&$x\mapsto \frac{1}{x-1}$\\
~\\
$h:\mathbb{R}\rightarrow \mathbb{Z}$		&$j:\mathbb{R}\rightarrow \mathbb{R}$\\
$x\mapsto \lfloor x \rfloor$					&$x \mapsto \pm\sqrt{x}+2$\\
~\\
$k:\mathbb{R}\setminus \{0\}\rightarrow \mathbb{R}\setminus \{1\}$	&$l:\{-4,-3,2,4,5,6\}\rightarrow \{0,1\}$\\
$x \mapsto \frac{1}{x}+1$							&$x\mapsto \text{remainder of }x/2$\\
\end{tabular*}

\begin{enumerate}
\item Identify which of the above maps are functions and which are not.  (If you do not remember the definition of a function consult page 139.)
\vspace{.3in}

\item Find the following (reference pages are given in parenthesis if you need reminders).
\begin{enumerate}
\item $f(3)$
\vspace{.3in}
\item (pg 141) the range/image of $f$ 
\vspace{.3in}
\item (pg 139) the pre image of 4 under $f$ 
\vspace{.3in}
\item (pg 141) $(f+g)(-1)$ 
\vspace{.3in}
\item (pg 141) $(fg)(x)$ 
\vspace{.3in}
\item (pg 146) $(f\circ g)(x)$ 
\vspace{.3in}
\end{enumerate}

\item (pg 141) Of the functions you identified in (1.) which are one-to-one/injections?
\vspace{.3in}
\item (pg 144) Of the functions you identified in (1.), which are bijections/has an inverse? Find the inverses that exist.
\vspace{1in}

\newpage
\item (pg 143) Create a function $m$ that is onto/a surjection but not one-to-one.
\vspace{1in}
\item (pg 145) \emph{Prove} that the function $g$ is one-to-one. 

\end{enumerate}
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