Any review sheet is a compilation of personal opinions about the relative importance
of various parts of the material. These are jason's. It would be crazy to rely on any
single resource to study for your Exam, including this little study guide!
Material covered on Exam 1:
Chapter 1, sections 1.11.8
Chapter 2, sections 2.12.6
with a ``lighter'' emphasis on sections 1.71.8 which discuss continuity and limits.
Section 1.1
Functions, linearity, proportionality
Some phrases which should give you that comfortable and confident familiar feeling:
``.
..is a function of.
..'', ``is not a function of,'' ``is inversely proportional to the square
root of'', ``has as its domain [4,6]'', ``is not in the range of'', ``constant rate of change'',
``by a table, a graph, a formula, and a verbal description'', ``the difference
quotient
'', ``is decreasing for negative
x
'', ``find the vertical intercept'', etc.
What's the domain of
? What's its range? How can you tell from a table whether
a function is linear? If it is linear, how can you find its formula? How is slope related
to increasingness/decreasingness of a linear function? Can you read the slope from a
graph? Can you read the
y
intercept? What's a constant of proportionality, and why
might you have to use one? And if you use one, how do you usually calculate its
value? How can you read domain and range from a graph? What does the Greek
capital Delta mean?
Section 1.2
Exponentials
Exponential functions have constant what? Here's one people seem to get wrong more
often than right: What's a continuous growth rate? What's a growth factor? If the
growth rate is 0.5, what's the growth factor? Which one appears on the general
formula
and which one appears in
? Speaking of these two, why
do we have two formulas for an exponential function? If I give you one, can you
convert it to the other? I like to think about this by analogy with the two forms of
linear functions: pointslope and slopeintersept form. What does concavedown
mean? How can you see it on a graph? on a table? What's that
? Yes, yes,
I
know
it's the initial value, but what does it represent in the context of any particular
problem? How can you tell at a glance whether a formula represents exponential
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View Full Documentgrowth or decay? Write an exponential function that starts really big and decays really
slowly.
Can you tell from a table whether a function might be exponential? How? If it is
exponential, how can you find its formula? (Careful, this is really easy in some
examples, but can be hard in others!) From two points on a graph can you find the
formula? It's fun to ask (ala 1.4.50) ``When will the population reach 5 million,'' or
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 Winter '05
 Staff
 Calculus, Derivative

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