Class: October 30, 2009

We started class with a warm-up of using different technology (calculator, Grapher, Wolframalpha, etc) and our intelligence to get as much possible information on the given rational function for a graph. We should be working our way to graphing these functions with only a pencil and ourselves!
Then we went over homework problems from last class: #43 and #47 (page 179).
After that, we got our quizzes back and went over them.
We then talked about the warm-up. The equation was x4-2x3-2x2-2x-3 / x3+6x2+11x-6.
We factored it into (x+1)(x-3)(x2+1) / (x-3)(x-2)(x-1), then divided it to find a slant asymptote of x+4. From there we continued to graph the function fully. Cool!
In the last couple of minutes we briefly went over graphing inequalities of rational functions (on tonight’s homework).

Check out this site for help with long division of polynomials!

Next scribe: Angus

Homework for next class:
Page 204| 11, 13, 15, 21, 37, 39, 43, 47, and 49
Don’t forget your Student Release Form if you haven’t passed it in yet!

October 28, 2009 What We Did In Class Today

For the first thirty minutes of class from 11:33-11:53. Next we took out our laptops and checked out rational functions. Homework will be due next Thursday November 5th, which is when we take the Unit Test.

Today we explored rational function: graphically, numerically, algebraically
We graphed two rational functions on Grapher. Which caused a frenzy in the class. We checked for domain, zeros, shape, asymptotes and other fun graphing things. After analyzing the functions we learned that one day we are expected to do this by hand... Oh no! The two programs we used today were Numbers and Grapher. We graphically analyzed first then we numerically analyzed.
Numerically: Find zeros: Find where numerator= 0. Find vertical asymptotes: Find where denominator= 0. To find the end behavior: Divide top and bottom by the largest power of x and let x--->infinity. After learning these steps we put them into practice and tried them out on some problems.

Homework ?’s that we didn't get to---43, 47


Homework for next class: p. 193/7, 11, 13, 15, 23, 37, 47, 57, 71 [Use your calculator and/or Grapher to explore- your goal should be to do each without technology on the quiz.]
If you forgot your permission slip, bring it in.
You can pass in your IOU’s at the beginning of next week.

Next scribe: Maci

Class - October 26, 2010

We began class today with a small warm up to practice our speed at checking answers in fractions, decimals, percents, and square roots without a calculator. Nick and Robin won (again). Following this we went over the Unit 2 Quiz #1 answers. It is important to realize when being asked for exact answers or not, what the standard form of an equation is, -b/2a, and what multiplicity is (how many times each zero occurs in a function).

Last quiz of the quarter on Wednesday that will cover everything we've had a chance to ask questions about from homework all from Unit 2.

We got to take a look at the Quarter 1 projects in the other class, W2, and see what those groups did. Make sure to indicate where you received help on the projects, as well as on homework and other class work.

Homework problems we went over in class: pg. 167 (39, 41, 43, 71)
39) a+bi complex conjugate is a-bi; helps to put i in front of the radical so you don't make it accidentally look like it's under the radical sign, which can become a very different number.
43) conjugate of the square root of 8 is the square root of 8.
71) If you don't like fractions, multiply the whole thing by the common denominator.
NEVER SQUARE ROOTS OF NEGATIVES IN YOUR ANSWERS! get rid of them as fast as you can. Also, make sure your answers with i are in the complex form, a+bi.

Class work problems for calc/non-calc: pg. 179 (12, 64) (goal is to do without a calc)
12) To find zeros with a calculator: trace if it is a whole number, or go 2nd Calc, zeros and then find. Also, go into data table and check by plugging in possible values of x to find a zero for y.
Without a calculator: use the Rational Root Test to find zeros with synthetic division or plugging in values.
Fundamental Theorem of Algebra introduced: if the degree of a polynomial function is n, then it has exactly n complex zeros, counting multiplicity.
You cannot divide a function to the power of 4 using synthetic division, must use real division (unfortunately).
Homework:

• p. 179/11, 13, 15, 37, 43, 47, 55, 63, 65
• Revise homework for quiz next class covering homework from 2.1-2.4

Next scribe: Kayla

Class, October 20

In class on Tuesday, we started with a warm up on page 149/42. We discussed how to graph polynomial functions without using a calculator, or grapher, etc., relating to the warm up. Next, we went over the homework, and any questions that the class had about the problems. After going over the homework, we took notes about polynomials and synthetic division, and the Remainder Theorem. The homework for the next class was:
pg. 159/ 8, 13, 21, 23, 25, 35, 37, 49, 59

*and there will be a quiz next class!!

Class October 22, 2009

For the first thirty minutes of class, we took a quiz on our homework from 2.1 and 2.2. We then went over how to use the remainder theorem of a fourth degree function and how to easily find any value like f(3) with synthetic division. We also went over homework problems from last class, and this lead us into a bit of a review on long division with functions and synthetic division. We went back and found the zeroes of the function f(x) = x⁴ – 3x³ + 3x² – 3x + 2, which lead us into a review of the forms of complex numbers. From there, we also went over how to add, subtract, multiply, and divide complex numbers and how to find the complex conjugate. We also learned that projects were due by midnight on Friday, not Thursday.

Homework:

• Be sure your project is ready to be graded by Friday midnight.
• p. 167/17, 19, 21, 29, 33, 37-51 odd, 65, 71

Next Scribe: I'm not quite sure. Has anyone not been scribe yet?