Leverage - Countdown Widget (300x250)

HW-
P=.8-true proportion
n=4-number of people polled
Find p(0), P(1), P(2), p(3), p(4)
Use nCr p^r(1-P)^(n-r)
Then use new formulas to find mean and standard deviation

Agenda-

• Went over HW
• People did #2 all parts on board (Mr. M told us we can't use parts of girls only whole girls)
• Go over HW 10 groups went up to board
• Adolfredo got an award and we got candy
• Did HW 11

Notes-
Mean of probability distribution-

=sum of Prob(all diff events)(Value of event)

Standard Deviation-



Announcements-
POW Due Wednesday

Next scribe is Christiana

Linear Interpolation 11.03.08

Today we learned how to do a different way of computing numbers that aren't on the "z table".

Notes:
Figure out how to compute whats going on at the point 1.65.




We know the z table values for both points 1.6 and 1.7.




With knowing those points, we use them to determine the value of 1.65

In this picture above, you can see the points 1.6 and 1.7 on the curve as well as the point we want to know. We connected the two known points with a straight line, which is the same as the point found between the two points on the curve.

z table values:

1.6 = 0.8904

1.7 = 0.9109

Now we take these two points z table values to compute the value for 1.65 as follows:

(0.8904 + 0.9109) / 2 = 1.8013 / 2 = 0.90065 -----> z value for 1.65

"This technique will work to find most points not on the z table" - Mr. Marchetti

Things done in class:

1. learned about linear interpolation
2. go over HW9
3. Classwork: A Normal Poll
4. Mean and Standard Deviation of Probability Distribution

Homework:

1. POW Revisions
2. Quiz on Wednesday (up through HW7)
3. Homework 10 (just introductory) and Read pg 410 both due on Thursday
4. POW: The Knights Switches due November 10

Next Scribe: Drew

Standard deviations and binomial distributions (11-04-08)

Today we mainly focused on binomial distributions and how to determine the values of Z on the table. For example, we worked on homework 9 and Mr. Marchetti explained how to find the "gaps in the table." Basically, if we want to find the number between Z=1.3 and Z=1.4, there is 1/3 of difference between them. Then we determine the value by getting the difference between the values of Z=1.3 and Z=1.4. Then we divided the difference by .33.
After discussing homework 9, we talked about "A Normal Poll," Alex explained how to find the probability that Harriet's poll will show Henry as the winner by using a standard distribution table. Since the true proportion was .6 and the standard deviation .069, we used ratios to get the probability. Alex moved the decimal point of sigma two places to the right, so he used the following equation: 1/6.9=x/10, after cross multiplying, x=1.45. He used the table as a reference to get the value of 1.45 SD from the mean. The value was 82.5, then he divided 82.5 by 2 and added the result to 50, this was equal to 92%.
Then Mr. Marchetti returned the graded POWs and announced that POW 10 will be due next Friday. There is no homework for tomorrow, but there's a quiz on standard distributions and binomial probabilities tomorrow.

The Circus (Oct 31/Halloween!)

We talked about our halloween costumes for a small while at the beginning of class. 

Next we did 'Back to the Circus' pg 402... this was about a circus woman who wanted to stop really close to a wall on a bike. She wants to know when to put the brakes on and she wants to hit the wall only 5 % of the time. to solve this you must use your brain or look below for the answer

100-10 = 90 %

you do this because the normal distribution chart calculates for both sides of the curve so therefore you need to subtract 5% from each side which = 10

look at the chart at 90% and you will see the number SD and estimate the number. I got 1.65 as the SD. Then do a ratio. 

      1 SD  divided by .3 meters = 1.65 SD divided by X meters

this makes X equal .49 and then you add 2 because that is the median and you get to stop at 2.49 meters. 

Also did HW 9 in class but going over those in class tuesday....................... NO HOMEWORK!!! But.... there is a quiz on wed.:

Binomial Probabilities

3 Person Polls

Graph

Normal Distribution

Up to HW 7 

No table stuff

Answer:

Why can we approximate binomial distribution with norm distribution?

Reminder... you can retake end functions with this quiz. 

Next scribe= Marcus P 

today in math

HW
Kings switches due 11/10
quiz wednesday
HW 9?

Today we had a wonderful hour and a half of math. Caitlin laughed, Lilli danced, keith sang a song about the heartland. Good times were had by all. Except for Camilla who huddled in a corner and cried like the little dark emo she is. But on a more serious note, let's talk mathematics. And imagine I'm tellin you this with an irish brooch.

Normal Table Page 398

This handy little table lists numbers of standard deviations, starting at zero and increasing by 0.1, and their corresponding area within the standard deviation of the mean. This comes in handy when finding percentages of natural functions that are between one and two deviations.

HW 8 Page 400

Using the natural table, we rationalized ways to find answers to questions similar to those we have done earlier in this unit. The main idea was finding percentages of graphs that lay between 1 and 2 deviations.

Back to the Circus page 402.

A circus stunt girl rides her bike towards a wall and would like to know how close she can start stopping while crashing only 5% of the time.

It was fun. Long live math

(Wednesday) October 29

Today:
Go over homework 6 & 7
More about normal curves

Next Class:
Finish discussing Classwork

Homework:
Quiz next Wednesday
Revisions due Thursday

Homework 6 (393) Means and More in Middletown
1) a) Only 2.5% of the houses cost over $950
b) 68% cost between $500-800
c) 13.5% cost between $350-500
2) 2.5%
3) 84%

Homework 7 (396) Gifts Aren't Always Free
1) The main idea that we are trying to explain to Craig is if the standard deviation was larger the deviation would be broader where as if it was smaller the deviation would be more concise.
2) $29-$24.50 is 68%

Classwork (397) Normal Areas
1) .38
2) .86

Class was the typical short Wednesday. We didn't actually accomplish much, but there was a pretty rad conversation about carrots going on at the next table. For the next class we'll finish where we left off in the Classwork on page 397.

Next Scribe:
Cody Ullrich (for Thursday October 30th)

Tuesday October 28
In Class:
-go over Homework 6
-Graphing Distribution (page 394) activity with TI-nspire

-Normal Areas (page 397)
-The Normal Curve (page 389)

Homework:
-revisions on test due Friday 31
-homework 7
-homework 8
(-there will be a quiz next week on this unit and end behavior. specifics will come later)


Review in Class of Normal Curves:
-68% of data falls inside the first diviation
-95% of data falls inside the second diviation
-2.5% are the sizes of the outer-most sections
(look at previous post by Ann to see pictures of a standard curve)

-if mean changes: the curve will shift to the left or right
-if standard diviation increases: the curve will spread and flatten out
-if standard diviation decreases: the curve will get skinnier and taller


New Information:


Graphing Distributions: (see page 394)

-the total area under the standard curve equals 1 unit
-finding a specific area under the curve gives a probability
-the area under the curve is called integration (or definitive integral)
-the following equation uses the mean and standard diviation to solve for a probablility of a result at any given interval (for example, on a standard curve if you want to find the probability of something happening between points a and b that do not land directly on a standard diviation 'line' you can use this formula to find the probability)

-for the simplest normal curve (a mean of 0 and standard diviation of 1) a simplified version of this formula can be used to find probabilities

(in class we experimented with these equations on the TI-nspire calculators, seeing how the curve changes as the standard deviation and mean get larger and smaller)

Normal Areas: (see page 397)

-this classwork deals with finding percentages of areas between two points, and also finding two points where a certain area would fall. (these problems were done through estimation in class)

The Normal Table: (see page 398)

- We read through this reference section in class and briefly looked at the table of "z number of standard deviations and corresponding area within that section. ("z" is just the value above or below the mean where a certain area is found. z values are equal to the area between 2 points)

Next Scribe: Nicole Anderson! (for Friday October 31)

Scribe Post- October 27- Period 1- Elizabeth C

The first thing we did in class was go over Homework 5. The big ideas for that were:

• As the number of people polled goes up, the percent that was in favor also went up


• The largest bars in the probability graph are the ones closest to the true proportion

Then we learned about the Central Limit Theorem:

Normal Distribution-

• Based on mean and Standard Deviation
• Represents probability of getting a result in an interval
• 68% of results fall within 1 deviation
• 95% will fall within 2 deviations

Inflection Point: The point where the curve switches from Concave up to Concave down.

Continuous Probability Distribution: When every point on the graph has a value(Like a bell curve)

Discrete Probability Distribution: When nothing happens between points (like a bar graph)

After this discussion, we did Deviations of Swinging while Mr. Marchetti checked the rest of the homework (Homework 12, 1, 2, 3 and the rational functions worksheet 380)

After that we whipped out the TI-nspires and did Graphing Distributions

Homework:

1. Revisions Due Thursday
2. Homework 6 and 7

Next Scribe: Kimmy

Friday October 24th

Announcements:

-Handed back World of Functions Test

-Quiz next week on beginning of Pollster's Dillemma

-There will be a section on next quiz that will allow you to retake the End Function's section on the last test. Mr. Marchetti will take your higher score out of the two End Function's sections and will replace your current grade on that section with the better score.

Notes:

We began taking notes on the normal distribution curve, like the one above. This picutre demonstrates the percent each section takes up of the data. The light gray represents 68%, the darker gray combined with the lighter gray represents 95% and all of the shaded portions combined together represent 98% of the data. The +1, -1 etc, demonstrates how many standard deviations that data point is away from the average, which is the middle line.

This picture demonstrates how many standard deviations each point is away from the mean.

Homework

1. Homework 6

2. Test Revision- Due Friday October 31st

Next Scribe Post: Gretchen Stulock

Blog for period 1 October 23th, 2008

Scribe: Taryn M



Agenda:

Go over HW 4

Return Rational Function Quizzes

The Theory Of Polls

Homework Check



We worked on The Theory of Polls and went over it in class. Mr.M only got half of the class done with the homeowrk check and he will do the rest on Monday.



* If you didn't do a good job on the quiz go talk to Mr.M about fixing it! There is a chnace you can retake parts of it.



Homework: Homework 5 and read pages 387-391



next scribe: Lizzy C

Scribe post for Wednesday October 22

October 22:Scribe- Miranda K

Agenda-

• go over hw 2 and 3
• theory of the 3-person poll

HW 3 big ideas:

• for each voter, the probability that the voter is in favor of your candidate is equal to the proportion in favor of your candidate in the overall population.
• if the overall population is big enough compared to the sample size we can approximate polling by sampling with replacement.
• if the population is big enough to justify the sampling with replacement, we need to limit our polling samples to 5%.

theory of 3 person poll is on p. 378. uses nPr and nCr

homework:

• homework 4
• homework check on thurs/mon. he is checking hw 1-3 in pollsters and stuff on end behavior, and inequalities

*scribe for thursday- taryn M.

Tuesday, October 7, 2008

Agenda

• Begin Pollster's Dilemma unit
• Unit problem
• Review rational functions
• Begin HW

Homework

• POW-A spin on Transitivity
• Quiz on rational functions on friday
• HW 1 & 2

***************************************************
In the Pollster's unit we will examine the validity of polls

• How polls are conducted
• Sampling-what it is, what it means
• Statistics of poll

In groups, read through unit problem and answer questions
***************************************************
Quiz topics

• Algebra of Rational Functions-add, subtract, multiply, divide
• Graphs of rational functions-Vertical Asymptotes, Horizontal Asymptotes
• End behavior
• Inequalities graphically or algebraically

Next scribe-Matt Sattler

Friday 10/3/08

Today in class, we went over the homwork from page 380, and then learned how to solve rational inequalities by algebra.

Solving Inequlities:

• Factor the inequality
• Find where the numerators x values equal zero, and the denominator's vertical asymptotes
• Create a number line using the values found above, going slightly beyond each of them
• Then test different numbers to see if they fit the inequality, and mark possible numbers
• Deterimine the solution based on these tests.

POW Rubric
E= M plus: one successful proof and adresses bullet 4 from part 2
M= Answers to numbers 1-3 with explanation, investigation with results for 2 0f 3 bullets in part 2, and attempts at proofs

The material on the test will be:
Graphing rational functions (asymptotes)
Algebra of rational functions
Inequalities (solving graphically and algebraically)

Homework:
POW due Wednesday
Test on 10/10/08
Review Packets
Next scribe is Joe

Monday 10/06/08

Notes:
We had a substitue in class today
We worked and finished The Pollster's Dilemma wich was handed out on a loose leaf sheet of paper by the sub
We worked for thirty minutes on the review sheet for the quiz
We also did HW1 from the Pollster's Dilemma unit in class
Homework:
Homework was HW2 from Pollster's Dilemma, POW 8, and to study for the quiz on Thursday
Announcements:

• Pow 8 due Wednesday 10/08/08
• Quiz over algebra of rational functions, graphing of rational functions, and end behavior of a function this Thursday 10/09/08

Quiz topic end behavior notes:

The end behavior describes how a graph appears as the independent variable approaches infinity to the right (x increases) or to the left (x decreases). It depends whether the degree of the polynomial is odd or even and the sign of the coefficient of the highest order term, an. The end behavior for all possible cases is:

• if the sign of the coefficient is positive and the degree is even, then y approaches positive infinity as x decreases and as x increases
• is the sign of the coefficient is positive but the degree is odd, then y apporaches negative infinity as x decreases and approaches positive infinity as x increases
• if the sign of the coefficient is negative and the degree is even, then y approaches negative infinity as x decreases and as x increases
• if the sign of the coefficient is negative and the degree is odd, then y approaches positive infinity as x decreases and approaches negative infinity as x increases
  
  

Next Scribe: Evan Anderson

Wednesday, October 1

Today in class we went over inequalities, one of which was x^2+3x-10/x^2-6x+9 < 0. When graphed, the equation goes below zero on the x-axis at (-5,0) and above again at (2,0) and has a vertical asymptote at (3,0). Therefore, the values for x when the function is less than zero can be expressed as -5 < x < 2.

HW: POW due Wednesday, October 8, and pg. 388 #1-14

Thursday, 0ctober 9

Agenda:

• Reveiwed Homework from wed.


• Quiz Review


• POW Rubric
  

Homework Review:

Today in class we reviewed homework from Handout 5.4, proplems 20, 23, and 24. These were all inequality problems.

20.


solution: x<-3

-2

Quiz Review:

We received and worked on review handout for the quiz next Thursday. The first has problems on the first page and an answer key on the second. The second is CH. 5 review and problems 1-14 are the most useful for review of horizontal and vertical, asymptotes, graphing functions, and finding end behavior (21-24 may also be useful).

• Quiz Thursday Oct. 9


• Graphing rational functions (asymptotes)


• Algebra of rational functions


• Inequalities (solving graphically is acceptable, but algebraically is best)

POW 8 Rubric

We also reviewed the rubric for POW 8 (included below).

• E= M plus: one successful proof and adresses bullet 4 from part 2


• M= Answers to numbers 1-3 with explanation, investigation with results for 2 0f 3 bullets in part 2, and attempts at proofs (may not be complete)

Homework

• POW 8- due thurs 10/2- wed 10/8


• Quiz review- Quiz on thurs 10/9

Tuesday, September 30

The agenda:
Review Friday's work
Review Homework 12
Learn how to solve equations/inequalities with rational functions

Homework:
POW due Fri-Wed
Quiz on Rational Functions 10/10
Revisit HW 12

Notes: Starting Pollsters Dilemma on Friday, just finishing Rational Function unit

End Behavior
x to the power of an odd number will give an equation like this

X^any even number:

Example of an exponential function (y=4^x):

Rational Function Review:

Bottom power is bigger-HA=0

Top power is bigger-no HA

Power is same-ratio of leading coefficients is HA

Solving Equations and Inequalities

Algebraically

Technology

Graphing or Table

Intersection on calculator: split equation into two with y equalling both halves, calculate intersection or look at data table for the same Y value

Algebra: cross multiply if fraction=fraction then simplify. If not, multiply both by LCD, input answers back into the initial equation and eliminate the extraneous "solution".

Next scribe is Ben K.

Answers to Questions

Hey all,

Thanks for the feedback and the great questions in class today. I thought that I would address many of them here so that everyone could see the answers. If I don't address your question here please let me know.

First of all for the review for the quiz, I wanted to find out where people felt their weaknesses were. It gives me information so that I can tailor instruction. So the review will focus on two areas, according to the feedback. These two areas pretty much encompass everything. They are:

• Graphing Rational Functions (including asymptotes and behavior)
• Algebra of Rational Functions

As for questions about grading. Here is a list of some of the frequently asked questions, answers:

Raising your grade

I allow the revision process to help students raise their grade. There will be no extra credit. You can revise the first POW and HW 8 even if you received an F on them. These will be the only assignments for which you can revise an F. If you revised an assignment and you did not receive a W (revised work) come see me and we can discuss a second revision. Quizzes and tests can be revised if you receive an R, but not an F.


Why does revised work only get a C?

Revised work only gets a C because I want to reward people who are able to meet my expectations the first time around. I also do not want people to rely on the revsion process alone (I was having problems with students only revising and getting to high a grade). Imagine you were a student who consistently got Ms on assignments anda student who always had to revise received the same grade, would that be fair?

These were the areas where people most had questions. I want to make one more point. I need more feedback from you. I need feedback in class, by asking questions, by answering them, and through your presentations. I had many index cards with people telling me that they are have serious difficulties. These students have not come for extra help and many do not ask questions in class. If I don't hear from you, I don't know if you need more practice, more time on a topic, more instruction, or if we can go on. Help me, help you to do better by giving me feedback. Emailing and texting would work to (just don't text me unless it is a serious school related matter)! Thanks.

September 26, 2008

There was a substitute teacher today.

Agenda

1. POW 8 : A Spin on Transitivity, page: 277
2. Read on Asymptotes, page: 288
3. Classwork: The End of a Function

Homework

1. Homework 12: Creating the Ending You Want, page:290, #'s 1 and 2

The POW is refering to transitive relationships. For example, if Joe is shorter than Kelsey and Kelsey is shorter than Matt, then Joe must be shorter than Matt. Another example would be, if $20 is greater than $10 and $10 is greater than $5, then $20 must be greater than $5. An example of a non-transitive relationship would be like a game of rock, paper, scissors. Where rock may be scissors, and scissors beats paper but then rock certainly cannot beat paper.

Post by: Elca Annis

Monday, September 29, 2008

Today in class we went over Homework 12. Then we took notes on solving equations, either algebraically or graphically on the worksheet page 380 on the Section Exercises 5.4:

• For question 1d. in Homework 12, one possible solution Mr. Marchetti showed us was the function
  

3. By graphing each side of this problem on the calculator with the first half of the problem before the equal sign as y1 and the 8 as y2 we were able to tell that these two equations intersected at x=.1621 and x=1.46, which is the solution



Unfortunately, the graphing method only gives approximations so it is better used as a way to check your answers.



6. We also solved this problem graphically in class to find intersections at x=2 and x=-7
If this problem were an inequality like this , the solution would be x<-7 Then we learned how to solve a problem algebraically: 2. To solve this problem, both sides have to be multiplied by (x-4) to eliminate the fraction




So then the equation looks like:




To finish solving, bring the 5x to one side and the 3 to the other:



-4x=-23 Then divide both sides by -4 so







10. The first step would be to factor wherever possible, so the new equation would be:


The next step would be to multiply each side by (x+4)(x-1)





After distribution, all like terms are gathered.





Since this equation is quadratic, 15 can be subtracted from both sides to make one side zero and the other side can be factored and solved from there.





To make one of the sides zero so the equation will be equal to zero,


or





The first answer to this problem is not relevant unfortunately, because the x=1 in the second fraction would be:

Which doesn't make sense because it is not possible to divide by zero. This problem can be checked by graphing the system which shows that at x=1, there is a vertical asymptote so it is not a possible anyswer, which is called an extraneous solution.



Homework:

• Worksheet page 380 choose 2 problems from Section Exercises 5.4 from questions 1-8 and choose 3 problems from questions 9-19. Solve each algebraically and then check them graphically.


• PoW 8 due any day from Thursday to Tuesday


• There is a quiz over functions on Thursday 10/9

The next scribe will be Maddy.

September 25, 2008

Today in class, we were first greeted with Mr. Marchetti telling us the proper way to add an equation to the blog posts. First, you click the 'add equation' button, then after you select a 'math' you edit the equation in the red font below the box, then you save it and copy and paste it into the blog post.
Then, we worked on POW 8 - A Spin on Transitivity, and discussed the transitive properties we explored earlier when we stated that if Keith is taller than Mr. Marchetti and Mr. Marchetti is taller than Camilla, than Keith must be taller than Camilla. Or, in mathematic terms: if a=b and b=c, then a=c. By the way, the black spots on the wheels on the POW are 1 for Betty's, 4 for Al's and 7 for Carlos. The POW will (tentatively) be due Thursday, but check your calendars and tell Mr. Marchetti if you have a conflict with turning it in on Thursday and he'll change the due date.
After we worked on the POW, Mr. Marchetti checked homeworks 9, 10, 11 and the packet work.
Later, we discussed 'End Behavior' which mainly deals with the horizontal asympototes of functions. We then found out that every function has two ends, negative infinity and positive infinity. This concept was further investigated on pages 288 and 289.
Our homework due Monday is Homework 12, and to do more problems in the packet.
The next scribe will be Ali Follett.

Today we took at quiz on tables, story sketches, algebra, and reciprocal functions.

Notes

There were no notes taken today

Homework

Revisions for Homework 8 are due tom (thursday)

There will be a homework check on Thursday and Monday from Homeworks 9-11 also including the problems that you have done from the packet

Keep doing problems in the packet that you have trouble with

Next Scribe is Emma

Scribe Post Per 8 9/23

Today
1.) Review HW
2.) Equations & Inequalitlies

HW
1.) Quiz tomorrow
- Up to Ch 11
- Rule of 4
-tables
-story sketches
- Reciprocal Family
- Algebra

Notes on Board
y=kx: linear function; direct variations
y=k/x: reciprocal function; inverse variations

domain: what X must be to make the function undefined (make the denomenator 0)

Horizontal Asymptotes
1.) biggest power of X on bottom means HA: y=0
2.) powers are the same in numerator and denomenator means look at the leading coefficients of the highest powers of X, because they are the HA's
3.) biggest power of X on top means no HA

Scribe Post 9/22/08

Class Notes



We started class today with a warm up: we had to find the common denominator for

[(x+1) / (x^2-5x+6)] - [(3x+11) / (x^2-x-6)]

and simplify

[(X^2-1) / (2x+2)] * [4/(x^2-2x+1)]

Next we went over some problems from the packet and disscussed vertical and horizontal asymptotes. Conclusively it was decided that several rules apply when finding the horizontal asymptote (HA) as x is getting damn big.

1. When the highest power of x is in the denominator the HA: y=0. Example: 1/(x^2+3)


2. When the highest powers of x are equal in the numerator and denominator use the coefficients in front of these values to find the HA. Example: (6x^2)/(3x^2+4) HA: y=6/3 or .5


3. When the highest power of x is in the numerator there is no horizontal asymptote, but there is a slant asymptote. Example: x^3/x^2. as x gets bigger the top and bottom continue to grow, so it just keeps going.

For HAs, however, there are some exceptions. For (x^2-9)/(x+3), a rule 3 case, there is no HA but when x=-3 the value is undefined. The graph of this appears to cross this line where the HA would be but there is actually a "hole," explained by the tern removable discontinuity.*plug this into the y= on your calculator to see the graph* Mr. Marchetti explains this using force fields. VAs are like star trek force fields that cannot be penetrated, while HAs are not. Close to zero they are weaker, but get stronger and eventually impenetrable farther away.

Announcements

Quiz tomorrow, wednesday, and Homework * revisions due thursday

Homework

Study for Quiz: Up to but NOT including rational functions, study tables, story sketches, reciprocal family, and algebra (used for tables) Also, due thursday are more problems from the packet, do some from the sections you need more practice on.

Next Scribe is Julia

gogolplex

For all of you wondering about how much gogolplex is, I found a page about it. ITS HUGE!!
Here's the link
http://www.procrastinators.org/oldsite/googolplex.html

Scribe for 18 Sept 2008

The first thing we did today was get back Homework 8: Mystery Tables, which most of the class got an R on, for lack of explanation. We will be able to revise them to earn points back. Today we also went over our worksheet about factoring with rational functions and all that fun stuff, which I'm not going to put on here because it would take a long time to explain, and there were just a few problems. Class went fairly well otherwise, expcept for the point at which we were sidetracked by talking about big numbers such as gogol and gogolplex and infinity, which prompted Mr. Marchetti to say, "We're talking about a HUGE number that makes damn big look damn small!"

Notes:

y=1/x+5 is undefined @ x=-5
the vertical asymptote (VA) is @ x=-5
the horizontal asymptote (HA) is @ y=0

for a more complicated rational function:
h(x) = 2/(xsquared + 4x +3)
the denominator can be factored as (x+3)(x+1) which can then be set to equal zero to find the vertical asymptotes:
(x+3)(x+1) = 0
x= -3, -1
VA: x= -3
x= -1
HA: y=0

some other notation-type stuff we learned was about infinity, which I don't know how to write on here, but essentially, it is phrased like this:

as x approaches infinity, y approaches 0
as x approaches negative three from the right, y approaches negative infinity
as x approaches negative one from the right, y approaches infinity

then the last thing we talked about was if we had really big numbers being plugged in for x. for example:
y= 5x+3/7x+5
x= a billion

5 billion/7 billion
billions cancel out
we're left with 5/7
so, as x approaches infinity, then y approaches 5/7

we also looked at the next POW 8: A Spin on Transitivity, which we will have a week and a half to do

Announcements:
We will have a test this coming Wednesday, the 24th of September

Homework:
Revise Homework 8 for next Thursday, start on POW 8, and from the rational functions worksheet, pick a few problems from each section of questions:
# 1-10
# 11-18
# 19-24
#25-34
# 41-46

Class Notes:

--------------------------------------

Multiplying/Dividing Fractions:

-REMEMBER: FACTOR FIRST

Multiplication example:

X+3/7 * 14/2X+6

2(X+3) <------ X+3 cancels

=1

Division Example:

7x-7y/4y / 14x-14y/3y

7x-7y/4y * 3y/14x-14y

7(x-y)/4y * 3y/14(x-y)= 3/8

Adding and Subtracting:

1. Find Lowest Common Denominator (L.C.D.)

2. Rename fractions (change denominator)

3. Add/Subtract

4. Simplify

Classwork (following notes):

-Pick 5 from numbers 39-52 (rationale packet)

-Pick 4 from numbers 53-62 (rationale packet)

-#28-38 odds

Homework:

-Quiz (next Wednesday)

-Rationale Packet

-Finish Classwork

Submitted: Matthew Sattler

September 17, 2008

Next Scribe: Erin Murray

World of Functions, Simplifying- Scribe for 9/17/08

Today was a short period so we just took notes and did some practice problems. 

Class notes: 

1. Simplifying: Remember to factor first! 

A. This concept is based in the basic simplifying fractions concept: keep dividing the numerator and denominator. 

**example: 24/72 --> 12/36 --> 4/12 --> 1/3 

B. To factor

** example: 24/72=(2) (2) (2) (3)/(2)(2)(2)(3)(3) 

**In this equation, you cross out the numbers that cancel out to be one to end with 1/3

2. How this applies to factoring equations

**example: x^2-10x+25 --> (x-5) (x-5) because you know that x^2= (x) and (x). You also know that -5 * -5 = 25 and -5+-5= -10

**Methods: The area model 

3. Steps to simplifying more difficult equations: 

a. Factor first!

b. Find common denominator 

c. Rename fractions

d. add or subtract 

e. simplify 

After these class notes we had time to practice some problems in the prerequisite chapter 42 practice packet. (This was given to us Monday in class.) 

Homework: In the prerequisite packet with the practice problems: 

-Choose 5 from 25-38

-39-49 odd

-Choose 4 from 53 to 62

Announcements: There will be a test next Wednesday the 24th. 

Scribe_Post

Briggs Buckley

World of Functions

Next Scribe - Matt Sattler

Homework Due –

• Homework 10 – Difficult Denominators
  
• Homework 11 – An Average Drive
  

Homework Assigned –

• Numbers 25 – 38 odds in Handout Packet
  

Class Agenda

1. Finish & Review “Return of the Shadow”
   
2. Go over Homework 10 & 11
   
3. Begin Rational Functions
   

Class Notes

1. Reviewed how to solve Return of the Shadow:
   
2. Notes – Domain: The set of all inputs that make sense
   

Comes from two places: 1. The function, and 2. The situation

Homework 10:

• Noticed Verticle asymptotes (A place where the function is undefined). Observations from the class concluded that the functions could get close, but would never cross the vertical line.
  

Homework 11:

• Class noticed both Vertical & Horizontal asymptotes.
  
• Noticed (through a horizontal asymptote graph, that as x gets bigger, y gets closer and closer to 25.
• The Class came up with two equivalent equations to help solve the homework:
  

y = 100 / 4 - (100/x) and y= 100x / 4x-100

Rational Functions:

• f(x) = P(x) / Q(x)
  
• Both the P(x) and Q(x) are polynomial
  

We Talked about:

• How to simplify
  
• The Domain / Range
  
• How to Add/Subtract/Multiply/Divide
  
• Graphs
  
• Find Common denominator when adding / subtracting
  
• Multiply straight across
  
• Stay, dot, flop when dividing
  

FACTOR FIRST!!!!!!! – Mr. Marchetti

Other Notes About the Day:

1. Zolla came in & made a call using a students cell phone
   
2. Joe & Zolla got into another heated politics debate (Zolla walked out)
   
3. Mr. Marchetti told everyone that he was 34 (there was discussion as to how young he looked… Mostly by Erin M.)
   

Friday, September 12, Period 8

Scribe_Post

Marcus P.

World of Functions

Next Scribe- Briggs Buckley

Homework Due-

• Homework 9: Bigger Means Smaller

Homework Assigned-

• Homework 10: Difficult Denominators
• Homework 11: An Average Drive
• POW 7: One Mile at a Time

Class Agenda

1. Go Over Homework 9: Bigger Means Smaller

• Family of Reciprocal Functions

2. Don't Divide That!

• Why doesn't dividing by zero make any sense?
• Look at the traits of the graphs, reciprocal functions

3. "Return of the Shadow"

*Hints

• Draw a diagram of the situation
• Use cross multiplication to find the missing component, the length of the shadow.

Family of Reciprocal Functions Notes

K=constant

Y = K/X

• y is inversely proportional to x, inverse variation

Y = KX

• y is directly proportional to x, direct variation

Monday, September 15, 2008

Agenda:

• Return of the Shadow
• Go over Homework 10 & 11
• Rational Functions

We had previously established that in order to solve this problem, we would use a pair of similar triangles from a diagram of the situation. We also found that as the height of the person increases, the shadow length does as well (i.e. height and shadow length are directly proportional.)

Next we set up proportions of the similar triangles to find the length of the shadow.

20/h= 12 + l / l (cross multiply. *note, cross multiplication can only be used when there
is an = sign!)

20l = h(12+l) (distribute the h)

20l = 12h+hl (subtract hl)

20l – hl = 12h (rearrange the equation into an equivalent situation)

l (20-h) = 12h --> l = 12h / 20-h (yay!!)

Domain Restrictions
Set of all x’s (inputs) that make sense in the function.
i.e. h cannot equal 20
h must be greater than or equal to 0
h must be less than 20

" 1 / damn big = damn small" -Carl Hostnik

Then we went over Homework 10 and reviewed asymptotes. We discovered that horozontal asymptotes can exist as well.

We reviewed Homework 11 next. We talked about an equation that applies to the homework and came up with two equivalent equations:

y = 100 / 4 - (100/x) and y= 100x / 4x-100

A horozontal asymptote occurs in this graph, as x gets really big, y gets closer to 25.

Last, we talked about Rational Functions!

• f(x) = P(x) / Q(x)
• P(x) and Q(x) are polynomial
• y= x*x+3x+4, or y= 4 / 9x
• a series of terms with a variable to a power of a whole number

We worked on some algebra, reviewing how to add/subtract, multiply and divide fractions.

Remember!

• Common denominator when adding/subtracting
• Multiply across
• Stay, dot, flop when dividing

Last, we worked on factoring rational functions.

ex. (x+3 / 7) * (14 / 2x+ 6) *2x+6 can be factored into 2(x+3)

2 * (x+3 / 7) * (14 / 2*x+3) = 1

• Next Scribe: ClaireH
• Homework: Practice Rational Functions worksheet, numbers 39-49 odds
• Quiz next Wednesday!!! Study!!

Tuesday, September 9th, Period 8

Scribe Post
-Lauren McDavid

-----------------------------------------------------------------

Announcements: None.
Next Scribe: Marcus Parry.

Homework Due: Homework 8.
Homework Assigned: Homework 9 (due Friday), POW Revisions (if needed, due Monday).

-----------------------------------------------------------------

Class Agenda:
I. Warm up (see below).
II. How to turn a table into a function notes.
III. Homework completion check. (Homework 1-8, except 5)
IV. Brake! Revisited (complete).
V. Learned about regressions (a calculator function).

-----------------------------------------------------------------

Warm Up:
1. (a+3b)2
a2 + 6ab + 9b2


2. (km+5k)2
km2 + 10k2m + 25k2


3. What kind of table is this?
X Y
2 11
4 31
6 59
8 95
10 139
12 191

Quadratic

-----------------------------------------------------------------

Table to a Function Notes:

1. Identify the family.
-->Common differences.

-->Common ratios.

2. Curve fitting.

-->Guess and check.

3. Systems of Equations

-->Quadratic, Cubic, etc.

4. Regressions.

-->Calculator.

5. Algebra.

6. Exponenial-ratio.

Scribe

Notes

Class Warm up:

We expanded equations.

I. E: (a+3b)^2

(a+3b) (a+3b)

From here, use F.O.I.L to fully expand the formula

F=First.

(a)(a)=a^2

O=Outer

(a) (3b)=3ab

I=Inner

(3b) (a)=3ab

L=Last

(3b) (3b)=9b



a^2+3b+3b+9b

a^2+6b+9b



We discussed discovering the family of certain tables. The example given was quadradic because the second differences were the same. Once we knew that the table was quadradic, we were supposed to find a formula for the table. We knew that the table would follow a quadradic function. We plugged the x values in for a the y values in for be and c always remained 1. We did this for three inputs and thus were given a system of equations. We solved the system and got the formula.



Homework

Finish Brake! Revisited and do homework 9.



ANNOUNCEMENTS

Revisions for POW 7, one mile at a time, are due monday. Remember to include the revised work as well as an explanation of what you did wrong and what you did to fix it.



Next Scribe

Camila S

Scribe Posts

One of your assignments this year is to be the scribe for the day. The scribe is responsible for adding a post to the blog that includes all of the information that was important for the day. Scribe posts should include:

• Notes
• Homework assignment
• Important dates and announcements

In addition you should label every post with three labels:

• Your name
• Kind of assignment (in this case scribe_post)
• Period (4 or 8)
• Unit (World of Functions)

Please comment on posts with questions, additions, or corrections. If you are absent check the blog to see what happened in class. Scribe posts are due by the next block. Failure to post will not only effect your responsibility grade, but your classmates as well.