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\noindent {\bf Math 181.8 First
Quiz}\hspace{1.7in}Name:\underline{\hspace{2.5in}}\\
\begin{enumerate}
\item Assume $f(x)=\sqrt{1-x}$ and $g(x)=x^2$ for the following:
\begin{enumerate}
\item[a)]Find the function $f \circ g(x)$.\\[.25in]
\item[b)]Find the domain of $f \circ g(x)$.\\[.25in]
\item[c)]Find the range of $f \circ g(x)$.\\[1in]
\item[d)]Find parametric equations for the path of a particle that moves
along the graph of the equation $y=f \circ g(x)$ starting at (1,0) and
ending at (-1,0).\\[.5in]
\item[e)]Find the function $f^{-1}(x)$.\\[1in]
\item[f)]How is the graph of the equation $y=f^{-1}(x)$ obtained from the
graph of the equation $y=f(x)$?\\[.25in]
\item[g)]Write the equation for the graph that is obtained by shifting the
graph of the equation $y=g(x)$ up by 2 units and to the right by 1
unit.\\[.25in]
\item[h)]Write the equation for the graph that is obtained by stretching the
graph of the equation $y=g(x)$ vertically by a factor of 3 and horizontally
by a factor of 2.\\[.25in]
\end{enumerate}
\end{enumerate}
\end{document}