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\theoremstyle{definition}
\newtheorem{definition}{Definition}[section]

\theoremstyle{convention}
\newtheorem{convention}{Domain Convention}[section]

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\begin{document}
\begin{center}

\Huge{Functions}
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\normalsize




\begin{definition} A \emph{function} $f$ is a rule that assigns to each element $x$ in a set A (called the \emph{domain}) exactly one element, called $f(x)$ in a set B (called the \emph{range}).
\end{definition}

\begin{convention}Then the domain is not explicit we use the domain convention: the domain of the function is the set of all possible inputs that the rule returns a real number.
\end{convention}

\noindent While working in a group make sure you:
\begin{packed_itemize}
\item Expect to make mistakes but be sure to reflect/learn from them!
\item Are civil and are aware of your impact on others.
\item Assume and engage with the strongest argument while assuming best intent.
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%{\large{Rules for engagement:}} (Underlying philosophy:  ``Growth Mindset")
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%\item Everyone shares their ideas. 
%\item Question \& challenge each other's ideas.
%\item Reflect on the strengths of each method appearing. 
%\item Mistakes are valuable, investigate them!
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\begin{enumerate}


\item Let $f$ be a function defined algebraically by: $\displaystyle{f(x)=\frac{1}{1-x^2}}$
\begin{enumerate}
\item Find $f(2)$ and $f(2.2)$.
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\item Find the output of the function $f$ when $x=-3$.
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\item Find $f(\triangle)$ and $f(a+h)$.
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\item Given that $f$ is a function, use the domain convention to find the domain of $f$?
\vfill
\end{enumerate}




\item Let $g$ be a function defined as: ``$g(x)$ equals the distance $x$ is from 0".
\begin{enumerate}
\item Find $g(3)$
\vspace{.5in}
\item Find the output of the function $g$ when $x=-4$.
\vspace{.5in}
\item What is the domain of $g$?
\vspace{.5in}
\item What other notation can you use to define $g$?
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\end{enumerate}

\newpage
Verify your answers for \#1 by looking at Example 5 from \S1.3.
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