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\centerline{Mathematics 133 -- Intensive Calculus for Science 1}
\centerline{Things to Know -- Exam 1}
\centerline{September 25, 2000}
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\noindent
Recall that the first full-period exam of the semester will be given 
in class on Friday, September 29.  There will be seven or 
eight questions similar to problems quizzes so far.
You should know the following material.  We will review for the 
exam in class on Thursday, September 28.
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\item{1)}  Linear functions and their properties (Section 1.2)
\itemitem{a)}  The slope-intercept ($y = mx + b$) and 
point-slope ($y - y_0 = m(x - x_0)$) forms for linear
functions
\itemitem{b)}  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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\item{2)}  Exponential functions and their properties (Section 1.3)
\itemitem{a)}  The general formula for exponential functions
$f(x) = ba^x$ (or using different letters, $P(t) = P_0 a^t$, as on page
17 of the text).  
\itemitem{b)} Exponential growth versus exponential decay (which values
of $a$ give which case)
\itemitem{c)}  Be able to determine an equation for an exponential
function, given a graph or a table of values.
\itemitem{d)}  How to tell exponential functions apart from linear functions
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\item{3)}  Power functions and their properties (Section 1.4)
\itemitem{a)}  Algebraic rules for exponents
\itemitem{b)}  The general form of power functions: $y = k x^p$
\itemitem{c)}  The general shapes of their graphs.
\itemitem{d)}  Which functions grow faster as $x$ grows: powers or
exponentials?
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\item{4)}  Inverse functions.  Know:
\itemitem{a)}  How to tell whether or not
a function is invertible from its graph, 
\itemitem{b)} How to derive
a formula for the inverse function $f^{-1}$ from a formula for $f$,
\itemitem{c)} How to sketch the graph of the inverse function from 
the graph of $f$.
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\item{5)}  The logarithm functions $f(x) = {\rm log}_a(x)$ and 
their properties
\itemitem{a)} $g(x) = {\rm log}_a(x)$ is the inverse function of the 
exponential function $f(x) = a^x$.
\itemitem{b)}  Formulas for logs of products, quotients, powers 
and how to apply them
\itemitem{c)}  The shapes of the graphs $y = {\rm log}_a(x)$
\itemitem{d)}  Using logarithms to solve equations involving
exponentials
\itemitem{e)}  The {\it natural logarithm function} $f(x) = \ln(x)$
(the logarithm function with base $a = e = 2.71828\cdots$)
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\item{6)}  Trigonometric functions.  Know:
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\itemitem{a)} Radian measure for angles and how to determine
the signs of $\sin\theta$, $\cos\theta$, $\tan\theta$ for an
angle $\theta$ in radians
\itemitem{b)}  How to sketch graphs for sinusoidal oscillations
$$y = A \sin(Bx) + C \qquad y = A\cos(Bx) + C$$
and the meanings of $A,B,C$
\itemitem{c)}  How to find a formula for a sinusoidal oscillation,
given the graph.  (Note: we have not talked about shifting the 
period to start at points other than $0$, so that will not be included)
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\item{7)}  Polynomials and rational functions.  Know:
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\itemitem{a)}  How to determine the shape of the graph of a polynomial
for big $x$ from the equation.
\itemitem{b)}  How to determine equations for polynomials given 
information from a graph such as $x$- and $y$-axis intercepts.
\itemitem{c)}  How to determine where rational functions have
vertical and horizontal asymptotes
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\noindent
Good Review Problems:
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From the Review problems at the end of Chapter 1:  1, 2, 6, 11, 22, 23, 24, 25, 27,29,
34, 35, 36,3 8, 39, 41, 44, 45

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From Section 1.10:  12 (sketch the graphs), 18 - 21
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