### The Adventure Continues ...

Our adventures in blogging continue....

Watch for 3 new blogs going live February 3, 2006 ...

- Applied Math 40S (Grade 12)
- Pre-Cal 40S (Winter '06) (Grade 12)
- Calculus 45S (Grade 12)

An interactive log for students and parents in my Pre-Cal 30S class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.

Our adventures in blogging continue....

Watch for 3 new blogs going live February 3, 2006 ...

- Applied Math 40S (Grade 12)
- Pre-Cal 40S (Winter '06) (Grade 12)
- Calculus 45S (Grade 12)

I'm so glad we've had this time together,

Just to have a laugh or learn some math,

Seems we've just got started and before you know it,

Comes the time we have to say, "So Long!"

So long everybody! Watch this space in February for pointers to new blogs for each of my classes.

Farewell, Auf Wiedersehen, Adieu, and all those good bye things. ;-)

Oh my sorry I totally forgot I was chosen to be scribe, well what can I say this last class was amazing we decided to do the podcast even if it was only Craig, Richard, Kasia and I…but it was great we still manage to do it haha well let’s see, the first part of the class was spent on doing the podcast and for the remaining of the class we did a pre exam test or w/e you call it and it really was helpful in many ways especially with reviewing some of the things that I’d had a hard time doing before, but man was it hard to do some questions without having a calculator but hey I managed…after that we were put into groups and were able to discuss the type of answers we got…and that’s where we ended our last class =( …I am so upset that math class is over because this year has been such a great experience I’ve met a lot of wonderful people that I’ve talked to in and out of class, and we all had our share or laughs either laughing with or at Mr. K and his jokes haha and or pointing and always choosing Richard for everything, etc overall I’d like to say that you guys are awesome and never change nor forget about the great times we had in pre cal class…and my last words would have to be exams start this Monday so good luck to everyone and I hope to see you all there! BYE…

We had our last class on Thursday and made a podcast to celebrate! We left ourselves a "pod capsule" in instead of a "time capsule."

Here is our Message in a Podcast (4 minutes, 26 seconds). Please leave any questions, concerns, complaints, compliments, confusions, uncertainties, anxieties or other inquiries in the comments to this post.

This isn't our last post yet -- I've got at least two more I want to get out before the end. ;-)

Hahaha...... Wow... To think I'd post here before an exam. Pretty Ironic eh? Oh shoot... Didn't finish my scribe post. lol. Yeah I did. But anyways... Before the Pod get's Cast's out of the school. I'd like to say... Bye to everyone again. Espically to the Study Crew. Haha. The Blogging Crew. And the MATH Crew. Hahaha. Which is all of you guys. Math won't be the same ever again. And if we don't blog... I start a blog. Hahaha. But... Also A BIG THANK YOU TO Mr. Kuropatawa. The best Math Teacher ever. I can't live with out his jokes. lol.

So I probably won't see you guys for about....... A year or so but... I'll be arround on the blog(s). The Sargent Park Grade 8 blogging run... Some other random blogs and I'll sneek into the PC40 Winter 06 blog to leave a ton of comments. Hahaha. Hey I'll even show up to PC40s on the first day back in Semester 2. Hahaha. Also ahhh... Nevermind. lol.

Well anyways.. I'd just like to say. Good-bye and... GOOD LUCK ON YOUR EXAM!!!!

Peace. Richard C.

Hey guys sorry this is late...

Well today in class we started off with a super secret survey! Whhooppeee! Well not really secret but close to. The survey was all about what we thought about the math class and teacher that happened to teach us. It was a simple circle the answer that best suits your thoughts on this topic type of thing until the end where you could right personal comments if you so wished. This was of course anomynous.

Next we were given a pre exam type pre test thing on what the class voted had been the hardest concept to understand...triginometry! This pre test was an awesome way in my opinion at least to help refresh our memories, because of this I feel that if you missed class today and the test I'm sure Mr. K would be happy to hand you a copy of it to do. I found that learning from the mistakes you made was way easier then watching Mr. K do the work on the board. I will post all the questions and answers tomorrow so that everyone else still doesn't miss out on the correct way of doing things.

Of course following the pre test we were split into groups and within them tried to figure out the best way to solve the problems. (Show you later on as I said)

Mr. K continued by showing us the answers on the board and going over only the first problem solving question (boy was that a doozy). The bell then promptly rang and class ended like any other day. :)

So you’re probably wondering... Why I asked Liz to pick me as scribe? Why am I scribing even before class started? and... Who am I in general? Well I asked Liz to pick me as scribe because I wanted to scribe one last time before Math ends. Hahaha. I’m going to miss math… *cries. Well anyways. To answer the second question. I have to make up for taking Liz’s math Dictionary right now. Hahaha… yes I’m sorry. Don’t blame Liz… Blame me. Haha… And also… The scribe for tuesday would be up at like… 12:00 Midnight because I get home at like 11:30 lol… (Unless I do it at lunch… Which is highly unlikely…) And My name is Richard. Well anyways… Tonight I scribe about Yesterday.

Well we had allot of notes… And allot of notes… And… A few jokes. (Anyone get the punch line) [Probably Not] {Dang I suck} We also had a story and a “pod casting news event” lol

We took allot of stuff in our dictionary… And because I forgot my glasses I took Liz’s dictionary instead… lol. Haha.

[Insert Example 1 - 4]

After that we took a visit to consumer math. One lesson we dare not learn… And put it in our Math Dictionary.

[Insert Consumer Math Diagram & Notes]

Well that’s it for tonight... Hehehe… Scribe tomorrow… Hehe…

Homework was the last exercise to whenever and Mr. K keeps on forgetting his pennies

Today.... We finished our Math Dictionary. AND..**END OF COURSE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!**

So... We had a good time the whole class. (AKA PARTY!!!)

Tomarrow's scribe is.... Kasia. Hahaha

ahh i wasn't aware that i was the scribe because i was the first one to be on the new cycle =\ . UNFORTUNATELY i can't make much of a scribe post because richard borrowed my dictionary . SORRY GUYS . BUT YEAH Today we wrote in our Math Dictionary's. Graeme's going to put that up. And Mr. K told us another story about a professor or somthing. After that the class was over. The next scribe is..... RICHARD because he wants to be again ? hah ..

Like sokoban the target is to push objects (in this case punt-discs or 'pucks') around a maze to cover various targets. In a punt maze however the pusher slides forward tilt-style until it hits an obstacle, and a puck that gets struck will be punted forward a matching distance.'

'Aim: Use the black cross as a pusher to 'punt' the yellow pucks onto the blue targets.

Movement: Use the arrow buttons provided to move the pusher (black cross). The pusher will run in a straight line until it hits a wall or a yellow puck. If it hits a puck the puck will be punted forward a matching distance.'

Are you ready to play?

(*Thanks again to* Think Again!)

So today we started off by talking about the coin hunt and how fun it was last year. Then he ask "who wanted to be part of the committee?"and how surprised he was when no one i mean no one raised there hand. Anyways we took out our handy- handy dictionary and discussed rational functions.

Graphing Rational Function

Rational Functions are written as the Quotient of two polynomial.

F(x) = __a(x)__ ; b(x) 0

. b(x)

appearance; f(x) = __1__ f(x) __1__

. n x^n*the graph will be posted shortly........*

where n is odd

where n is even

Sketching:

step1: Factor everything if possible

step 2: find the y- intercept (let x= 0)

step3: find the roots of the function by finding the roots of the numerator [ a(x)]

step4: find the vertical asmptote( s) by finding the roota of the denominator [b(x)]

step 5: find the horizontal asymptote.

case1: degree of a(x)<>

horizontal asymptote @ y= 0

case 2 : degree of a(x) = degree of b(x)

Horizontal asymptote found by: __leading coefficient of a(x)__

. leading coefficient of b(x)

case 3: degree of a(x) > degree of b(x)

no horizontal asymptote there may be a "slant asymptote" or a hole in the graph.

Step 6: Do a sign analysis of the function over the intervals defined by the roots and vertical asymptotes.

step 7: Sketch the graph

and the 4 examples we're doing tomorrow. and was it for our dictionary.

as the fraction gets smaller the product increases.

the denominator is getting closer to 0.

the answer is getting closer to infinity.

example:

1/1/10 = 10

when you divide by 0 you get infinity. You are not allowed to divide by zero because you can't get infinity as an answer. infinity is not number.

Then next thing we knew the bell rang......

oh yeah the scribe for tomorrow is ..........................

rannell d. hope you have fun!

Well I know that it Aichelle's scribe stated that Larisa's today's scribe, but apparently she has already been scribe so Aichelle chose me to be today's scribe =/.

Anyway today's class started off regulary with Mr. K puting questions on the board for us to do for a little review from yesturday's class, but today's class was kind of weird for the start. We only had ONE question to work with. Kind of odd don't you think ? Usually it would be the whole white board with 4 questions or sometimes just 2, but today we had only 1 ? I think Mr. K believes we're getting the hang of things here. Question: Do you Mr. K ? Anyway we should be starting to get used to them anyway from the homework and reviewing our notes. HINT HINT exam less than 2 weeks, time to test our long term memory guys.

4x^{3}-7x+3 <--- that was the question from today. I will put up the process later today just because I feel like annoying you guys and making you work at it and not just copying it down =D.

EDIT: Solution

y-intercept @ y=3

possible numberators: ±1, ±3

possible denominators: 1, 2 ,4

possible roots: 1/1, -1/1, 3/1, -3/1, 1/2, -1/2, 3/2, -3/2, 1/4, -1/4, 3/4, -3/4

f_{(x)} = (x-1)(4x2+4x-3)

f_{(x)} = (x-1)(2x-1)(2x+3)

roots @ x = 1, 1/2, -3/2

Then you graph it, lol it's not because i'm lazy to put in the graph myself but I think we all should be able to create the graph using our calculators. IE. extra practicing using our calculators =D**Edit done**

Afterwards Mr. K gave us the schedule for the rest of the week:

Today: Polynomial Function graphing notes and start on ~~Radical~~ Rational Functions

Tomorrow: Continue ~~Radical~~ Rational Functions, graphing and notes

Friday: Finishing off the rest of our notes and finishing off the cirriculum.

Today we had A LOT of notes written down in our dictionaries, mine came to about 2 and a half maybe 3 pages ? lol, but they were in-depth so they should help us when we study for our exam.~~Radical~~ Rational functions we started with Mr. K explaining to us why we can not divide by the number 0. It is because if we divide by 0, 0 can be any number.

ie.

2 *2 = 4

4/2 = 2

2*0 = 0

0/0 = 2 <--- CAN'T HAPPEN

Afterwards we then began to look at the graph of this function, f_{(x)} = 1/x, and saw that it never touches 0. It gets close and close and closer to 0 but never touches it. This lead to Mr. K's lesson of "The History of Google," which is acually a number that looks like this 1x10^{100}. Lol I know I cheated but I'm not going to sit and count 100 zero's lol it's lunch time I still have to eat ;). And that is how class ended today with Mr. K yelling (exageration) out our homework while we piled out of the classroom. (Homework Ex. 56)

BTW tomorrow's scribe is...... Robinna =P

and a little reminder**ODD POWERS CUT THROUGH THE X-INTERCEPT, AND EVEN POWERS BOUNCE OFF THE X-INTERCEPT.**

something I thought might help =D

Today’s class started off with Mr. K. handing back our project evaluations. He also talked about acrostics for this unit. Yesterday we learned how to graph a polynomial function without a calculator or started to learn how and today we did some more of that.

Important stuff to know:

-The maximum number of roots a polynomial function can have is the number of the highest degree in the polynomial [ex. x²+6x+9~the maximum number of roots this equation can have is 2]

-the end behavior determines which way the arms of the function go [like in a parabola if the end behavior is positive then the arms go up but if it is negative the arms go down]

-polynomial functions are smooth and continuous-they have no jagged points

-the Fundamental Theorem of Algebra says that the number of roots a function has to have is the highest degree in the function [like x³~this has to have 3 roots]

—but not all polynomial functions have roots, they have complex/imaginary roots.

This then brought Mr. K. to talk about how we should stay in math when we go to university/college and he also talked about jobs—for more info go read his blog post:http://pc30s.blogspot.com/2006/01/why-should-i-learn-math_17.html

After that we finished drawing the polynomial function without using a calculator that was on the board yesterday by doing this in these steps: [pictures may be blurry just click them]

We then got this sketch by plotting the roots and the y-intercept onto the grid and drawing the function’s basic shape:

After that Mr. K. put a question on the board that we had to do by ourselves which was draw f(x) = x³ + 3x² -13x – 15 without using a calculator. To figure this out you need to follow the same steps as in the question above ^. If you did then you got something like this:

The last function we had to graph without our calculator was f(x) = 2x^4 + x³ - 17x² - 16x + 12. We only got so far as to find the y-intercept [@ 12] the possible numerators [±1, ±2, ±3, ±4, ±6, ±12], the possible denominators [1, 2], the possible roots [±1, ±2, ±3, ±4, ±6, ±12, ±1/2, ±3/2], and we also did some synthetic division but we didn’t get to finish the whole thing because we ran short of time due to the bell, so Mr. K. said we will go over the question tomorrow.

Homework is Ex. 54 [1, 2, 3] & Ex. 55. [and if I made any errors or mistakes just let me know, thanks] ohhh and the scribe is:

This is taken from an article (Math Will Rock Your World) from Business Week. A few snippets:

Y'wanna get a really interesting job working with people on lots of interesting things?

But just look at where the mathematicians are now. They're helping to map out advertising campaigns, they're changing the nature of research in newsrooms and in biology labs, and they're enabling marketers to forge new one-on-one relationships with customers. As this occurs, more of the economy falls into the realm of numbers. Says James R. Schatz, chief of the mathematics research group at the National Security Agency: "There has never been a better time to be a mathematician."

Learn math!

How'd ya like a six figure salary?

...new math grads land with six-figure salaries and rich stock deals. Tom Leighton, an entrepreneur and applied math professor at Massachusetts Institute of Technology, says: "All of my students have standing offers at Yahoo! (YHOO) and Google (GOOG)."

Learn math.

D'ya wanna to work on the biggest most cutting edge issues of our day?

This mathematical modeling of humanity promises to be one of the great undertakings of the 21st century. It will grow in scope to include much of the physical world as mathematicians get their hands on new flows of data .... "We turn the world of content into math, and we turn you into math," says Howard Kaushansky, CEO of Boulder (Colo.)-based Umbria Inc., a company that uses math to analyze marketing trends online.

Learn math.

Y'wanna make one of the most significant contributions to the betterment of humanity?

"The next Jonas Salk will be a mathematician, not a doctor."

Learn math.

What are the implications for k-12 education?

Outfitting students with the right quantitative skills is a crucial test facing school boards and education ministries worldwide. This is especially true in America. The U.S. has long leaned on foreigners to provide math talent in universities and corporate research labs. Even in the post-September 11 world, where it is harder for foreigners to get student visas, an estimated half of the 20,000 math grad students now in the U.S. are foreign-born. A similar pattern holds for many other math-based professions, from computer science to engineering.

The challenge facing the U.S. now is twofold. On one hand, the country must breed more top-notch mathematicians at home, especially as foreigners find greater opportunities abroad. This will require revamping education, engaging more girls and ethnic minorities in math, and boosting the number of students who make it through calculus, the gateway for math-based disciplines. "It's critical to the future of our technological society," says Michael Sipser, head of the mathematics department at Massachusetts Institute of Technology. At the same time, school districts must cultivate greater math savvy among the broader population to prepare it for a business world in which numbers will pop up continuously. This may well involve extending the math curriculum to include more applied subjects such as statistics.

Learn more math!

"But I don't like math. Besides, I don't need it. I'm going into the humanities or business!"

As mathematicians expand their domain into the humanities, they're working with new data, much of it untested. "It's very possible for people to misplace faith in numbers," says Craig Silverstein, director of technology at Google. The antidote at Google and elsewhere is to put mathematicians on teams with specialists from other disciplines, including the social sciences.

Just as mathematicians need to grapple with human quirks and mysteries, managers and entrepreneurs must bone up on mathematics. Midcareer managers can delegate much of this work to their staffers. But they still must understand enough about math to question the assumptions behind the numbers. "Now it's easier for people to bamboozle someone by having analysis based on lots of data and graphs," says Paul C. Pfleiderer, a finance professor at the Stanford Graduate School of Business. "We have to train people in business to spot a bogus argument."

Ya gotta learn more math!

Yes, it's a magnificent time to know math.

'Nuff said.

Okay, I know it's late, but I just got home for the first time since 8:30 this morning so please bare with me. Also to add to my frustrations Firefox is lost on my harddrive and I dont have enough time to dig it out or re-download it so I'm going to have to do this without pictures or diagrams.

So, it all started off with Mr. K. going around and handing out the "Go For Gold" assignment. Just as a reminder:

-Must get 100%; anything else is unacceptable.

-You can recieve help from anyone at any time on this assignment

-Copying other people's work is completely unacceptable

-Due Monday, January 23, 2006

Then, we had to take some notes into our dictionaries. They were:

-Remainder Theorem

-Factor Theorem

-Synthetic Division

(I will not write the notes in this post, because that's Graeme's job and I don't want to steal his chocolates!)

Following this we continued with today's concept:

GRAPHING FUNCTIONS W/O A CALCULATOR!!!

~We first learned a couple properties of the graphs of functions:

- All even exponents for the equation ( y=x^n ) look like parabolas ( U-Shaped)

- All even exponents for the equation ( y=x^n ) have 3 points in common: (-1,1); (0,0); and (1,1)

- All even exponents for the equation ( y=x^n ) have a minimum of 0 roots.

- All odd exponents for the equation ( y=x^n ) look like cubics (attétude position)

- All odd exponents for the equation ( y=x^n ) have 3 points in common: (-1,-1); (0,0); and (1,1)

- All odd exponents for the equation ( y=x^n ) have a minimum of 1 root.

*Note* The maximum number of roots that a function can have is equal to "n" in the equation ( y=x^n ).*

Finally, we briefly learned about the "Descartes Rational Root Theorem". However, I did not quite understand this so I will only provide the example we were taught and hopefully tomorrow Mr. K. will teach us some more about it.

EXAMPLE: ƒ(x) = 3x^3 - 4x^2 - 5x + 2

Possible Numerators( taken from the the positive and negative factors of the last term): ±1, ±2

Possible Denominators ( taken from the positive factors of the coefficiant of the first term): 1, 3

Possible Roots:(Hope This Works!)

1 ,-1, 1 ,-1, 2 ,-2, 2 ,-2

___ __ ___ __ ___ __ ___ __

1 , 1 , 3 , 3 , 1 , 1 , 3 , 3

Then you check by a new form of Synthetic Division:

* | 3 -4 -5 2

_____________

1 |3 -1 -6 -4 x

-1| 3 -7 2 0 √

.: 3x^3 - 4x^2 - 5x + 2 = (x+1) (3x^2 - 7x +2)

Well that about wraps it up, I'm very sorry, but I was very busy tonight and it didn't help that I've lost Firefox, so thank you for baring with me and I'll try to fix the problems right away.

Oh yeah! By the way there's a couple things (reminders) for Mr. K.

1. Tests back

2. Assignments back ( Mathland)

3. New Acrostic Words

Thank You

and the next scribe is...

Aichelle

Well here I go again doing my scribe post. Sorry that it's so late!! Well todays class started off with two questions. Question 1. (a) on the Factor and Remainder Theorems sheet and a question on the board. We then did the questions together as a class and went through the answers. After that we went into our dictionaries and wrote some notes. (Those notes will we posted or added to Graeme's massive notes post. Don't forget to thank him once again and give him his chocolates.) As class went on we continued writing our notes. Mr. K gave us our homework and then class was over.And the next scribe is CRAIG!!

Thanks go out to Mrs. Armstrong for pointing to today's game from Think Again!.

The game, from Japan, is called **Slither Link**.

Rules of Slither Link

1. Connect adjacent dots with vertical or horizontal lines.

2. A single loop is formed with no crossing or branches.

3. Each number indicates how many lines surround it, while empty cells may be surrounded by any number of lines.

Play here.

hahahaha HAPPY BIRTHDAY TO RICHARD *a.k.a.* ORCHARD *a.k.a.* REESHARD* a.k.a.* RICO SWAVI *a.k.a.* RICKY* a.k.a.* MALCOLM X* a.k.a.* ROY!!

So today in class Mr. K layed out exactly what he wanted to get done. It seemed that division was the "theme" of the day. So first there was the review of last class and grade 5 and 10 division which would be the topic for the class. He gave us the following problems:

Then after we had finished those he asked us if we could see a pattern in relation to the P(-2) for a), P(1) for c) and a P(3) for c) of the numerator of each of those functions that he gave to us and the remainder. Then Craig (of course) had found it and told us, it seems that the answer that was in the numerator after the evaluation had been complete was the remainder! Now we needed a bit more information on how this happens and Mr. K obliged us. It seemed that after a bundle of explaining if you take the root of the denominator and put it in the numerator of the division question and solve you will get your remainder. I don't know if I explained it well but it will have to suffice as my explanation. That would be the Remainder Theorem.

Well I was thinking... "And the use of this is...?" He then went onto explaining his point with the grade 5 problem. The answer to the problem is 718. It takes 3 of those to give you 2154. Well those two numbers they are factors of 2154. Well that also works with polynomials. If it divides evenly then you have factors of that polynomial (no remainder). Which can be useful I guess. That would be the Factor Theorem.

Well we never did get to the Grade 11 way of doing the division but that will be done tomorrow and the scribe for that will be

.... *Drumroll*.........

Today in class we continued off the notes that we did not finish off yesterday and this was what we wrote.**Many-to-one function**

more than one member of the domain

is mapped to a single member of the range. (I could not upload the image because there was an error and I don't know what it is)**One-to-one function**

Function where each (one) member of the domain is mapped to a unique (one) member of the range.

(same thing happened I could not do it)**Horizontal line test**

Used only on the graphs of functions. (i.e the vertical line test has already been satisfied).

sweep a horizontal line across the graph of any function if the line crosses the graph more than once the function is many-to-one if the line crosses the graph everywhere exactly once then the function is one-to-one.

*Relations FunctionsMany-to-one---------One-to-one*

A FUNCTION CAN BE LOOKED UP AS A GRAPH, EQUATION, AND TABLE OF VALUES.

One-to-one functions are "special" because they are always "invertible".

Inverse: - the inverse of any operation returns a value from its result to its original value.

- the inverse of a function "undoes" what the original function did.

Example 1:

clean room----------------------messy room }domain

BABY PLAY----------------------PARENT CLEAN-UP

messy room----------------------clean room }range

BABY PLAY and PARENT CLEAN-UP are inverses of each other. Each "undoes" what the other one "does".

NOTATION: given any function f(x) its inverse is written as f-1(x) (-1 is a power more like a square but different)

IMPORTANT: f-1(x) can not equal 1/f(x)

REMEMBER: given any function f(x) and its inverse f-1(x), the domain of f is the range of f-1 and the range of f is the domain of f-1 (see example 1)

Given any ordered pair (x,y) its inverse is (y,x). Given any function defined in a table of values, the inverse function is found by exchanging the domain and range.

Example 2:

x----y

(-2)--(-1)

(-1)--(1)

(0)--(3)

(1)--(5)

(2)--(7)

x----y

(-1)--(-2)

(1)--(-1)

(3)--(0)

(5)--(1)

(7)--(2)

1-

Example 3: Find the Inverse of y=2x2-3

finding the inverse

x=2y2-3

x-3=2y2

x-3/2=y2

square root of x-3/2=y

so that was it for today but the notes are unfinished and we will finish tomorrow in class.

OH YAH DON'T FORGET GraemeW CHOCOLATE BARS TOMORROW

Since GraemeW is getting chocolate bars tomorrow u can be the SCRIBE FOR TOMORROW.

HAVE FUN

Well today... Like OVER HALF THE CLASS WAS GONE!!! (doing an English exam) So... We fooled around and partied the hole class!!!! Hahahaha. Just kidding. Well we partied until I mentioned the scribe post... Then they elected me as scribe... Thanks guys... Robert... Hahaha Well anyways.. Today in Class.. We. Talked like forever... On math... and it was fun... Hehehe...

Anyways... We did questions... Hahaha... Questions on functions that we did yesterday.

Question #1

Question #2

Question #3

Well figure them out... Hahahahaha. Answers will be posted at 10:00 ;) Hahaha.

After that we put some Function notes in or Handy Dandy Dictionary. Hahaha... (couldn't resist)__Functions____Function:__ A function is a rule that changes one number or expression (The Input) into another number or expression (The Output)

The set of all possible __inputs__ is called __the domain.__

The set of all possible __outputs__ is called __the range.__

Functions (as opposed to relations)

Are rules that nave a special constraint:

Each member of the domain (the inputs) is mapped to (can be changed into) only one number of the range (only one output).__Notation:__ f(x) means "the rule f is appilied to a number or expression x."__Many-to-one Functions__

Functions where more than one (many) members of the domain are mapped to a single (one) member of the range.

So then... The bell rang... and he never finished... Hahaha. Then... Yeah... My new name is... Richard, Roy, Malcolm, Orchard, Rico Swavi, Von-E-Rechard, Rechard, Kraimer, Ricky etc... etc... etc..

Hahaha.. Math was fun today... lol.

Well I'm out. NO HOMEWORK!!! Unless you want to figure out those questions. Hahaha. Remember Answers at 10. Hahaha. Later.

Oh yeah... Tomarrow's scribe is... YESTERDAY'S SCRIBE!!!!!

And that is... **ABDI**

Oh I almost forgot... SUPRISE QUIZ TOMARROW!!!

HAHAHAHAHA... Just Kidding :P

10:00... ANSWER KEY

Well we started off the new year with a new unit. FUNCTIONS!

A function is a rule that puts in an input and give only **1** output. You can determine its a function by doing a verticle test line, and if it touches the graph just **once, **then it is a function.

All functions are relations, but not all relations are functions.

An example of a relation, that is a function is:

An example of a relation, that is **not** a function is:

When Adding or Multipyling functions, order in which you put them in **doesn't** matter, this is called the **Commutative Law.**

When Subtracting or Dividing, order in which you put them in **does** matter because it can result in different answers.

With that said if you are given 2 elemenatary functions:

Adding them:

Subtracting them:

Mulitplying them:

Dividing them:

Well this is all I got for now, if there is anything missing or something is wrong, please feel free to correct me. It's the beginning of coming back from 2 weeks off, so there's probably more things missing then usual. (hehe..)

The next scribe is Abdi

I found this "test" over at Teaching and Developing Online. Try it out .... just for fun. ;-)

Below are four (4) questions and a bonus question. You have to answer them instantly. You can't take your time, answer all of them immediately.

OK?

Let's find out just how clever you really are. No looking at the answers in advance.

Ready? GO!!! (scroll down)

First Question:

You are participating in a race. You overtake the second person.

What position are you in?

Answer:If you answered that you are first, then you are absolutely wrong!

If you overtake the second person and you take his place, you are second!

Try not to mess up in the next question.

To answer the second question, don't take as much time as you took for the first question.

Second Question:

If you overtake the last person, then you are...?

Answer:If you answered that you are second to last, then you are wrong again. Tell me, how can you overtake the LAST Person?

You're not very good at this! Are you?

Third Question:

Very tricky math! Note: This must be done in your head only.

DoNOTuse paper and pencil or a calculator. Try it.

Take 1000 and add 40 to it. Now add another 1000. Now add 30.

Add another 1000. Now add 20. Now add another 1000 Now add 10.

What is the total?

Scroll down for answer.

Did you get 5000?

The correct answer is actually 4100.

Don't believe it? Check with your calculator!

Today is definitely not your day.

Maybe you will get the last question right?

Fourth Question:

Mary's father has five daughters: 1. Nana, 2. Nene, 3. Nini, 4. Nono.

What is the name of the fifth daughter?

Answer:Nunu?

NO! Of course not.

Her name is Mary!

Read the question again.

Okay, now the bonus round:

There is a mute person who wants to buy a toothbrush. By imitating the action of brushing one's teeth he successfully expresses himself to the shopkeeper and the purchase is done.

Now if there is a blind man who wishes to buy a pair of sunglasses, how should he express himself?

He just has to open his mouth and ask, so simple.

So simple it is ... ;-)