My "preview" turned out to be a fairly accurate guide to what would show
up on the exam. So I've included it here, along with a few minor
additions.
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Here are some things you can expect to show up on the second exam. None
of this will be too surprising, since we spent time on all of these topics
in class and on the homework.
* At some point you'll probably have to find all the rational and/or
real and/or complex roots of a polynomial.
* You should know the Rational Zeros Theorem, Descartes' Rule of Signs,
Remainder Theorem, and the other tools used to find the zeros and
factors.
* You should know what odd/even zeros are, and what their geoemtric
interpretation is when you graph polynomials.
* Once you can find zeros of polynomials, you can find zeros and
vertical assymptotes of rational functions. You should know what
the geoemtric interpretation of an odd/even zero in the numerator
or denominator is. (Note that we talked about even zeros in
the denominator in class, but it's glossed over in the book.
Check your notes from class.)
* You should be able to find and describe the end behavior of a polynomial
or rational function. I'm not likely to have you do in-depth
long division of polynomials, so the "fast" way from lecture
would probably be appropriate.
* I should mention that _synthetic_ division will almost certainly
be necessary on the exam at some point, probably when finding
zeros of some polynomial. [Update: if you don't know synthetic
division, but you can do long division of polynomials, that's fine.
It just takes a little bit longer...]
* Composite functions and inverse functions could show up in the
multiple choice or long-answer sections of the exam, or both.
* You'll need to be comfortable with logarithms and exponents, through
the "properties" in section 4.5. Sections 4.6 and later are
officially off the exam.
* Notice that 2.6 is officially on this exam, but I haven't yet decided
whether a problem from this section will show up. There's
probably enough for you to do with chapters 3 and 4. However,
in the "spirit" of this section, I could use words to describe
a certain problem in terms of polynomials and ask you to write
down the correct equations before solving it.
(I know, I know... word problems: ick.)