Information about Quiz 3

• Reminder: There is a quiz on Wednesday, October 14. If you do not drop this quiz, it will count for 6% of your grade for the course. The quiz will take 30 minutes and covers sections 2.5, 2.6, 2.7 Because this quiz has a lot of graphing questions, CALCULATORS WILL NOT BE ALLOWED.

  The important topics covered in these sections are:

  1. Complex Numbers --- How to add, subtract, multiply and divide them. Solving quadratic equations with complex roots

  2. The Fundamental Theorem of Algebra

     Correspondence between zeros and factors of a polynomial
     Factor a polynomial completely over C
     Factor a polynomial completely over R
     Complex roots occur in conjugate pairs
     Factor a polynomial completely given one root
     Construct a polynomial with integer coefficients and a specified list of roots

  3. Graphing Rational Functions

     shifting, stretching and reflecting basic graphs such as

      1      1      1     1
     ---,   ---,   ---,  ---, ...
      x     x^2    x^3   x^4
     

     If we don't have simple shifts etc of these standard functions then we factor the numerator and denominator and determine x- and y-intercepts; vertical, horizontal and/or slant asymptotes if they exist; sign changes. Then put the pieces together to sketch the graph of the function.

  4. Finding Partial Fraction Decompositions of Rational Functions will not be on this quiz.