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\centerline{Mathematics 131 -- Calculus for Physical and Life Sciences 1}
\centerline{Exam 1 -- Things to Know}
\centerline{September 17, 2004}

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{\it General Information}

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\item{$\bullet$}
The first exam of the semester will be given 
on Wednesday evening, September 22 at 6:00pm, in Haberlin 103
(the large lecture hall on 1st floor Haberlin), subject to 
approval of the Registrar.  You will have
until 7:30pm to work on the exam if you need that much time.
\item{$\bullet$} Alternate time for those who have conflicts:
Wednesday evening, September 22,  7:30pm - 9:00pm.  If neither time works 
for you, contact me as soon as possible to arrange for another
time to take the exam.
\item{$\bullet$}
This exam will cover the material we have studied
since the start of the semester -- sections 1 - 6
of Chapter 1 in the text.  (See below for a more
detailed breakdown of the topics to know.)  
\item{$\bullet$} A
basic scientific (non-graphing) calculator will be
provided for your use on the exam.  Some questions
will ask you to determine possible formulas for given graphs
based on the properties of the ``library of functions''
we have studied in class.  {\it Be prepared for questions 
of this type}.
\item{$\bullet$} You will not be allowed to use
cell-phones, computers, or other electronic
devices during the exam.  If you bring your cell-phone,
please {\it turn it off} before the exam is handed out.

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We will review for the 
exam in class on Wednesday, September 22 or possibly
Tuesday, September 21 if people prefer.  

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{\it Material To Know}

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You should know the following topics:

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A) Functions, linear functions and their properties (Section 1.1)
\medskip
\item{1)}  The domain and range of a function, and how
to determine them from a graph or formula.
\item{2)} The slope-intercept ($y = mx + b$) and 
point-slope ($y - y_0 = m(x - x_0)$) forms 
for linear functions
\item{3)} The meaning of the slope and how to determine 
it from either a formula for the function, or from a table of values
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B) Exponential functions and their properties (Section 1.2)
\medskip
\item{1)} The general formula for exponential functions
$f(x) = ca^x$ 
(or using different letters, $P(t) = P_0 a^t$, 
as on page 11 of the text).  
\item{2)} Exponential growth versus exponential decay (which values
of $a$ give which case)
\item{3)} Be able to determine an equation for an exponential
function, given a graph or a table of values.
\item{4)} How to tell exponential functions apart from linear functions
\item{5)} How to use exponential functions to model quantities
that are growing or decaying at a constant rate
\bigskip
\noindent
C) New functions from old via horizontal and vertical
shifting, or stretching/shrinking (Section 1.3)
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\noindent
D) Composition of Functions, Inverse functions.  (Section 1.3) Know:
\medskip
\item{1)}  How to compute a composition $f(g(x))$ and identify
when a function is formed this way.
\item{2)} How to tell whether or not
a function is invertible from its graph, how to derive
a formula for the inverse function $f^{-1}$ from a formula for $f$, and
how to sketch the graph of the inverse function from  the graph of $f$.
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E) The logarithm functions $f(x) = \log_a(x)$ and 
their properties (Section 1.4)
\medskip
\item{1)} $g(x) = \log_a(x)$ is the inverse function of the 
exponential function $f(x) = a^x$.
\item{2)} Formulas for logs of products, quotients, powers 
and how to apply them
\item{3)} The shapes of the graphs $y = \log_a(x)$
\item{4)} Using logarithms to solve equations involving
exponentials, including in ``story problems'' on 
quantities that are growing or decaying at a constant rate
\item{5)} The {\it natural logarithm} function $f(x) = \ln(x)$
(the logarithm function with base $a = e = 2.71828...$)
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\noindent
F) Trigonometric functions (Section 1.5).  Know:
\medskip
\item{1)} Radian measure for angles and how to determine
the values of $\sin(t)$, $\cos(t)$, $\tan(t)$ for an
angle $t$ in radians
\item{2)}  How to sketch graphs for sinusoidal oscillations
$y = A \sin(Bx) + C$ or  $y = A \cos(Bx) + C$
and the meanings of $A,B,C$
\item{3)} How to find a formula for a sinusoidal oscillation,
given the graph.  
\bigskip
\noindent
G) Power, polynomial, and rational functions (Section 1.6) Know:
\medskip
\item{1)} How to find $x$ and $y$-axis intercepts, ``end behavior'',
etc. from the formula
\item{2)} How to to find a formula for a polynomial or a ``simple'' rational
function, given the graph. 

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{\it Some Good Review Problems}

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From the Review problems at the end of Chapter 1:  1, 2, 6, 7, 8, 11, 15,
22, 23, 26, 27, 31, 33, 35, 37, 38.

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The ``Check Your Understanding Problems'' at the end of Chapter 1
are also very good for studying.
\bye
