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. --------------------------------------------------------------------- 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.)