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\begin{document}

\title{MTH 1410, Fall 2011}
\author{Chapter 1 Review }
\date{}
\maketitle


\section{Activity Description}

Work out each problem on your own.  After you have completed it (or become totally stuck), find someone else and introduce yourself.  Compare your answers (or have them help you figure out the answer), then sign each other's papers and move on to the next problem.


\section{Problems from Section 1.1}

\benu
\item The graph below shows the height of the water in a bathtub as a function of time.  Give a verbal description of what you think happened.
\vspace{3.5in}
\begin{flushright}
\underline{\hspace{1.5in}}
\end{flushright}
\newpage


\item Let $f(x)= 4+ 3x-x^2$. Evaluate the difference quotient $\d\frac{f(3+h)-f(3)}{h}$ and simplify your answer.

\vspace{4in}
\begin{flushright}
\underline{\hspace{1.5in}}
\end{flushright}
\item Sketch the graph of the function
$$f(x)= \begin{cases} x+2 &\mbox{if } x\leq -1\\
		x^2 &\mbox{if } x>-1 
		\end{cases}$$
		Do not use a graphing calculator.

\vspace{3in}
\begin{flushright}
\underline{\hspace{1.5in}}
\end{flushright}

\newpage


\item Find a formula for the described function and state its domain: A rectangle has perimeter 20 meters.  Express the area of the rectangle as a function of the length of one of its sides.
\vspace{3.5in}
\begin{flushright}
\underline{\hspace{1.5in}}
\end{flushright}
\section{Problems from Section 1.3}

\item The graph of $f$ is given.  Draw the graphs of the following functions:
\benu[(a)]
	\item $y=f(x)-2$
	\item $y=f(x+1)$
	\item $y=-2f(x)$
\eenu

\vspace{3in}
\begin{flushright}
\underline{\hspace{1.5in}}
\end{flushright}
\newpage


\item Use the table to evaluate each expression:
\[
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
x & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline
f(x) & 3 & 1 & 4 & 2 & 2 & 5 \\
\hline
g(x) & 6 & 3 & 2 & 1 & 2 & 3 \\
\hline\end{tabular}
\]
\benu[(a)]
	\item $f(g(1))$
	 \vspace{.5in} 
	 \item $g(f(1))$
	\vspace{.5in}
	\item $g(g(1))$ 
	\vspace{.5in} 
	\item $(f\circ g)(6)$
\eenu
\vspace{.2in}
\begin{flushright}
\underline{\hspace{1.5in}}
\end{flushright}
\item A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 60 cm/s.  

\benu[(a)]
	\item Express the radius $r$ of this circle as a function of the time $t$ (in seconds).
	\item If $A$ is the area of this circle as a function of the radius, find $A\circ r$ and interpret it (note: $A\circ r$ should be a function of $t$).
\eenu

\vspace{3.5in}
\begin{flushright}
\underline{\hspace{1.5in}}
\end{flushright}

\newpage


\section{Problems from Sections 1.5 and 1.6}

\item Under ideal conditions a certain bacteria population is known to double every three hours.  Suppose that there are initially 100 bacteria.
\benu[(a)]
	\item What is the size of the population after 15 hours?
	\item What is the size of the population after $t$ hours?
	\item Estimate the size of the population after 20 hours.
	\item Estimate the time for the population to reach 50,000.
\eenu
\vspace{3.5in}
\begin{flushright}
\underline{\hspace{1.5in}}
\end{flushright}
\item Solve the equation for $x$.
$$e^{7-4x}=6$$

\vspace{2.5in}
\begin{flushright}
\underline{\hspace{1.5in}}
\end{flushright}

\eenu






\end{document} 