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\centerline{\textbf{Exam \#1 study guide $\cdot$
Math 124 $\cdot$ Calculus I $\cdot$ Section 26 $\cdot$ Fall 2008}}

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Disclaimers about the study guide:

\begin{itemize}

\item Exam 1 covers sections 1.1 through 2.1.  While all \emph{topics} on the
exam will be taken from this study guide, the specific \emph{questions} on the
exam will not be identical to the ones you see here.

\item In addition to consulting this guide, please review all homework problems
for sections 1.1 through 2.1.  In particular, look at unassigned problems
nearby.  For example, if I assigned \#14, see if you can do \#13 and \#15.

\item For reference, you can: (*) use the back of the book; (*) use the student
solution manual; (*) make use of the tutor center in Math East 145; (*) ask
questions in class; (*) talk to me after class, or during office hours.

\end{itemize}

John Kerl \\
\texttt{kerl.john.r@gmail.com} \\
2008-09-10

\begin{center}* * *\end{center}

Topics:

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\begin{itemize}

\item Point-slope and slope-intercept forms for equations of lines.

\item Composing and decomposing functions.

\item Inverse functions; meaning of inverse functions including units.

\item Solving a pair of equations by eliminating a variable.

\item Given a pair of data points, come up with a linear equation going
through those points.

\item Given a pair of data points, come up with an exponential equation going
through those points.  (Note:  I might not give you a $y$-intercept.)

\item Solve an exponential equation using logarithms.

\item Properties of logarithms.

\item Transformations of functions: shift, scale, reflection.

\item Drawing qualitative graphs:  i.e. I give you a verbal description,
without numbers, and ask you to sketch a graph.

\item Definitions of amplitude, vertical shift, period, and horizontal shift
for a sine or cosine function.

\item Given information about a sine or cosine equation, come up with an
equation which models the data.

\item Given a sine or cosine equation, sketch a graph.

\item Domain, zeroes, horizontal asymptotes, and vertical asymptotes for
rational functions.

\item Intuitive definition of limit:  as $x$ approaches some value $c$, does
$f(x)$ approach some finite value?  If so, the limit exists.

\item Definition of one-sided limits and two-sided limits; computing/estimating
them from a graph or data table.

\item Intuitive notion of continuity on an interval:  can you sketch the graph 
(or part of it) without picking up your pencil?

\item Definition of continuity at a point:  If the function $f(x)$ is defined
at a point $c$, \emph{and} if $\lim_{x\to c} f(x)$ exists, \emph{and} if the
two are equal, \emph{then} the function is continuous at that point.  If
\emph{any} of those three isn't true at $x=c$, then $f(x)$ isn't continuous at
$c$.  (It might still be continuous somewhere else.)

\item Intuitively:  if you can tell what the value of the function $f(x)$
``should'' be at a point $c$, given its surroundings, and if you can tell what
the value of the function $f(c)$ is, and if those two are the same, then the
function is continuous at $c$.

\item Difference quotients and average velocity (algebraically) as slopes of
secant lines (geometrically).  Know the definition and be able to compute
specific values.

\item Instantaneous velocity (algebraically) as the limit slopes of secant
lines (geometrically).  Know the definition and be able to compute specific
values.

\item Graphical interpretation of $f'(a)$, given a formula, data table, or
graph of $f$.

\item Estimate $f'(a)$, given a data table or graph of $f$.

\end{itemize}

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