We'Ve CoMe To An EnD aGaIn ??? =((( Oh WeLlL...

HEY MY FRIENDS AND ALSO MY DEAR TEACHER..SO IT SEEMS WE HAVE COME AGAIN TO AN END TO ME GUIDING YOU ALL IN ANOTHER CHAPTER OF ADVANCED FUNCTION. AND I KNOW I WILL NOT BE SEEING YOU ALL AGAIN IN THIS BLOG. NIWAYS, HOPE I HAVE HELPED YOU ALL IN SOME WAY TO UNDERSTAND SOME HARD PARTS OF ADVANCED FUNCTION. GUD LUCK FROM ME TO ALL OF YOU ALL IN YOUR STUDIES AND HOPE WE MIGHT MEET AGAIN IN ANOTHER BLOG NEXT TIME..BUBYE!! ~.~ :))

LaSt SuBtOpIc FoR tHiS cHaPtEr :D

HEY EVERYONE :) SO WE HAVE COME TO THE LAST SUBTOPIC OF THIS CHAPTER, THERE'S NOTHING MUCH THAT IS DIFFERENT IN THIS SUBTOPIC. WE STILL HAVE TO FIGURE THE VALUES OF ANGLE OF x. ONLY THIS TIME WE GET COMPLICATED EQUATIONS IN WHICH WE HAVE TO FACTORIZE OR SIMPLIFY TO GET THE VALUE sin x, tan x AND cos x. THE REST OF THE WORKING IS THE SAME AS LEARNED IN THE PREVIOUS SUBTOPIC. ONE OTHER THING IS THAT THE INSTANTANEOUS RATES OF CHANGE OF A SINUSOIDAL FUNCTION FOLLOW A SINUSOIDAL PATTERN.

LaSt SuBtOpIc FoR tHiS cHaPtEr :D

HEY EVERYONE :) SO WE HAVE COME TO THE LAST SUBTOPIC OF THIS CHAPTER, THERE'S NOTHING MUCH THAT IS DIFFERENT IN THIS SUBTOPIC. WE STILL HAVE TO FIGURE THE VALUES OF ANGLE OF x. ONLY THIS TIME WE GET COMPLICATED EQUATIONS IN WHICH WE HAVE TO FACTORIZE OR SIMPLIFY TO GET THE VALUE sin x, tan x AND cos x. THE REST OF THE WORKING IS THE SAME AS LEARNED IN THE PREVIOUS SUBTOPIC. ONE OTHER THING IS THAT THE INSTANTANEOUS RATES OF CHANGE OF A SINUSOIDAL FUNCTION FOLLOW A SINUSOIDAL PATTERN.

MaKiNg CoNnEcTiOnS aNd InStAnTaNeOuS rAtE oF cHaNgE :)

HEY GUYS, I KNOW THAT IT IS SUPRISING THAT I'M POSTING THIS VIDEO RIGHT NOW, AS IT IS ABOUT THE LAST SUBTOPIC IN THE CHAPTER WE'RE LEARNING NOW..MS JOANNE HAVNT TAUGHT US THIS SUBTOPIC YET..HOWEVER, AS I'M TOO FREE, I THOUGHT WHY NOT JUST POST THIS VIDEO FIRST HUH..MAYBE SOME OF YOU WANNA HAVE A LOOK AT IT TO GET SOME IDEA ON IT BEFORE WE LEARN MORE ABOUT IT IN CLASS..SO HAPPY WATCHING @ LEARNING GUYS :DDD

SoMeThInG fAmIlIaR?? yeAhHh..OnLy We'Ve LeArNeD iT iN dEgReE FoRm ^^

HEY EVERYONE, I'M BACK HERE AGAIN WITH YOU ALL AFTER A LONG AND BUSY WEEKEND. WELL, WE STUDIED ON HOW WE SHOULD SOLVE TRIGONOMETRIC EQUATIONS TODAY. IN A WAY,TODAY'S LESSON MIGHT BE REVIEW FOR MOST OF YA..CAUSE WE HAVE STUDIED THESE BEFORE..ONLY IN DEGREE FORM. HOWEVER, WE'RE LEARNING THROUGH RADIAN PROCESS RIGHT NOW..

THERE'S NOT MUCH FOR ME TO POINT OUT IN THIS CHAPTER. TRIGONOMETRIC EQUATIONS CAN BE SOLVED ALGEBRAICALLY BY HAND OR GRAPHICALLY WITH TECHNOLOGY. THEY ARE OFTEN MULTIPLE SOLUTIONS. MAKE SURE YOU FIND ALL SOLUTIONS ACCORDING TO THE GIVEN DOMAIN IN THE QUESTIONS. SOMETIMES, THE SOLUTION YOU GET MIGHT BE BIGGER OR SMALLER THAN THE GIVEN DOMAIN, SO MAKE SURE YOU DON'T INCLUDE THEM. AND ONE MORE THING IS, QUADRATIC TRIGONOMETRIC EQUATIONS CAN OFTEN BE SOLVED BY FACTORING.

SO TO FURTHER ENHANCE YOUR UNDERSTANDING ON THIS FAVORITE SUBTOPIC OF MINE IN THIS CHAPTER, I HAVE INCLUDED A VIDEO FOR YOUR VIEWING..CHEERS!! :)

AnD aFtEr 2 DaYs Of StUdYiNg AbOuT sInUsOiDaL fUnCtIoNs..HeRe YoU gO!!! :)

SO, WE WERE TAUGHT IN CLASS FOR 2 DAYS REGARDING THE 3RD SUBTOPIC OF THIS CHAPTER...SINUSOIDAL FUNCTIONS OF THE FORM f ( x ) = a sin [ k ( x - d ) ] + c AND f ( x ) = a cos [ k ( x - d ) ] + c...

ACTUALLY, THERE ISN'T MUCH TO REMEMBER IN THIS SUBTOPIC EXCEPT THE MEANINGS OF THE VARIABLE IN THE SINUSOIDAL FUNCTIONS..SO HERE ARE THE MEANINGS OF EACH VARIABLE..
|a| IS THE amplitude
d IS THE phase shift
c IS THE vertical translation
THE PERIOD OF A TRANSFORMED FUNCTION IS GIVEN BY 2π/k.

I'M ALSO INCLUDING A GRAPH ON THIS SUBTOPIC TO MAKE YOU ALL UNDERSTAND MORE ABOUT IT :)

GrApHs Of ReCiPrOcAl TrIgOnOmEtRiC fUnCtIoNs...

LeT's ExPlOrE tHrEe MoRe TrIgOnOmEtRiC fUnCtIoNs :D

TODAY, WE LEARN ABOUT 3 MORE TRIGONOMETRIC FUNCTIONS AND THEIR PROPERTIES. THESE GRAPHS ARE y = csc x, y = sec x, and y = cot x. THESE 3 GRAPHS ARE RECIPROCAL GRAPHS AND THEY ARE RELATED TO THE GRAPHS OF THE 3 PRIMARY TRIGONOMETRIC FUNCTIONS. THESE 3 GRAPHS ARE ALSO PERIODIC. NOW, I WOULD LIKE TO ATTACH EXAMPLES OF HOW THESE 3 RECIPROCAL GRAPH WOULD LOOK LIKE..

GRAPH OF y = csc x...

GRAPH OF y = sec x...

GRAPH OF y = cot x...

 NOW THAT YOU HAVE ALL SEEN HOW THESE 3 RECIPROCAL GRAPHS LOOK LIKE, THERE ARE SOME KEY FEATURES THAT WE SHOULD NOTE. RECIPROCCAL TRIGONOMETRIC FUNCTIONS ARE DIFFERENT FROM INVERSE TRIGONOMETRIC FUNCTIONS BECAUSE...
~ csc x MEANS 1/sin x WHILE sin^-1 x ASKS YOU TO FIND AN ANGLE THAT HAS A SINE RATIO EQUAL TO x
~ sec x MEANS 1/cos x WHILE cos^-1 x ASKS YOU TO FIND AN ANGLE THAT HAS A COSINE RATIO EQUAL TO x
~ cot x MEANS 1/tan x WHILE tan^-1 x ASKS YOU TO FIND AN ANGLE THAT HAS A TANGENT RATIO EQUAL TO x

GrApHs Of SiNe, CoSiNe AnD tAnGeNt FuNcTiOnS...

ThE bEgInNnINg Of ChApTeR 5 :)

SO HAVE STARTED CHAPTER 5 AT LAST. THE FIRST SUBTOPIC IN THIS CHAPTER IS GRAPHS OF SINE, COSINE AND TANGENT FUNCTIONS. FIRST OF ALL, LET ME ATTACH IMAGES OF GRAPH y = sin x, y = cos x and y = tan x FOR YOUR BETTER UNDERSTANDING..

GRAPH OF y = sin x

GRAPH OF y = cos x

GRAPH OF y = tan x

KEY POINTS OF THIS SUBTOPIC : -
~ THE GRAPHS OF y = sin x, y= cos x, and y = tan x ARE PERIODIC.
~ THE GRAPHS OF y = sin x AND y = cos x ARE SIMILAR IN SHAPE AND HAVE AN AMPLITUDE OF 1 AND A PERIOD OF 2π.
~ THE GRAPH OF y =sin x CAN BE TRANSFORMED INTO GRAPHS MODELLED BY EQUATIONS OF THE FORM y = sin x + c, y = a sin x, y = sin ( x - d ), and y = sin k x.
~ SIMILARLY, THE GRAPH OF y = cos x CAN BE TRANSFORMED INTO GRAPHS MODELLED BY EQUATIONS OF THE FORM y = cos x + c, y = a cos x, y = cos ( x - d ) and y = cos k x.
~ THE GRAPH OF y = tan x HAS NO AMPLITUDE BECAUSE IT HAS NO MAXIMUM OR MINIMUM VALUE. IT IS UNDEFINED AT VALUES OF x THAT ARE ODD MULTIPLES OF π/2, SUCH AS π/2 AND 3π/2. THE GRAPH BECOMES ASYMPTOTIC AS THE ANGLE APPROACHES THESE VALUES FROM THE LEFT AND THE RIGHT. THE PERIOD OF THE FUNCTION IS π.

I'm BaCk !!! YeAyYyY!!!

HEY EVERYONE!!! I'M BACK IN MY BLOG ONCE AGAIN. THE TIME HAS COME AGAIN FOR US TO DWELL ON THE WORLD OF ADVANCED FUNCTION AND THIS TIME I'M GONNA HELP YOU ALL IN UNDERSTANDING CHAPTER 5 OF ADVANCED FUNCTION: TRIGONOMETRIC FUNCTIONS ^^ FIRST OF ALL, I'VE GOTTA SAY, THAT THIS CHAPTER IS MY HARDEST PART IN ADVANCED FUNCTION..SO I WILL TRY MY BEST TO GUIDE YOU ALL IN REMEMBERING THE IMPORTANT POINTS ON THIS CHAPTER AND IN THE SAME TIME LEARNING MORE ABOUT THEM..SO HOPE YOU ALL WILL ENJOY THIS LEAARNING RIDE WITH ME ..ALL THE BEST !!!

EnD oF cHaPtEr 1??? oH wElL =(

HAHA...SO WE HAVE COME TO THE END OF CHAPTER 1 NOW...TODAY'S LESSON WAS BLENDED LEARNING...IT WAS A NEW OF EXPERIENCE..IT WAS A BIT HARD TO USE THE GEOMETRY SKETCHPAD AT FIRST..BUT AFTER THAT WE UNDERSTOOD THE CONCEPT AND WE COULD COMPLETE THE GIVEN WORKSHEET..SO I GUESS TOMORROW WILL BE THE LAST DAY FOR ME TO COMMENT ON THIS BLOG..WILL BE GIVE MY "FAREWELL SPEECH" TOMORROW OKIE :)

QuIz!!!!!!!!!!!!! OhHh NoOoOo *-*

OHHH YEAH...THERE WAS NO LESSON TODAY CAUSE WE HAD QUIZ...SHOULD I CALL IT SCARY??? NAHH...NOT YET...THIS IS JUST A QUIZ RIGHT?? IT'S NOT A 'TEST'...THEN PERHAPS I COULD CALL IT SCARY..MAYBE :P TODAY'S QUIZ WAS FOR ABOUT HALF HOUR..I WAS A BIT WORRIED IN THE BEGINNING CAUSE I DID NOT STUDY YESTERDAY..I ONLY FLIPPED THROUGH MY BOOK TODAY MORNING...BUT LUCKY ME I FOUND THE QUIZ A BIT EASY..SO ALL WAS WELL (JUST HOPE THE MARKS ARE ALL WELL TOO :P)!!! AND BESIDES THAT MS.JOANNE GAVE US SOME INFO ABOUT THE BLENDED LEARNING THAT WILL TAKE PLACE EVERY MONDAY..WE MAY NOT HAVE TO COME TO CLASS BUT THERE WILL BE ASSIGNMENTS ON BLACKBOARD 7 ABOUT OUR WORK FOR THE DAY..SO WE HAVE BEEN TOLD BY MS. JOANNE THAT OUR WORKSHEET ON MONDAY WILL BE ABOUT TRANSFORMATIONS..IT'S A BIT OF WHAT WE STUDIED IN HIGH SCHOOL AND CONTINUATION OF OUR LESSON ON PREREQUISITE SKILLS..IT'S GONNA BE A NEW LEARNING EXPERIENCE..HOPE IT CAN BENEFIT US..SO EVERYONE..I WILL BE BACK ON MY BLOG ON MONDAY..LALALA ~

CAN EQUATION BE CONFUSING??

LIKE THE TITLE ??? HAHA...THE ANSWER TO MY QUESTION IS NO...IF U REALLY WUNDERSTAND WHAT THE CONCEPTS OF EQUATIONS ARE..IT'S FUN TO STUDY THEN..TODAY'S LESSON WAS QUITE SIMPLE I THINK CAUSE THERE WHERE NOT MANY INFOS..JUST UNDERSTANDNG THE LESSON..WE STUDIED ABOUT SLOPES OF SECANTS YESTERDAY BUT TODAY IT WAS SLIGHTLY DIFFERENT..WE STUDIED ABOUT SLOPES OF TANGENTS AND HOW IT CONNECTS TO INSTANTENOUS RATE OF CHANGE..

INFOS..OH INFOS ~

SLOPE OF SECANT LINE = SLOPE OF TANGENT LINE

AS SLOPE OF SECANT LINE INTERSECTS WITH SLOPE OF TANGENT LINE, THEIR INSTANTENOUS RATE OF CHANGE IS THE SAME

INSTANTENOUS RATE OF CHANGE = VELOCITY OF THE GRAPH AT THAT POINT

WeLl..ThIs Is MoRe LiKe WhAt I sTuDiEd LaSt TiMe :)

TODAY WE LEARNT SOMETHING OLD..DO YOU REMEMBER ABOUT GRADIENT THAT WE STUDIED IN HIGH SCHOOL LAST TIME??? WELL, TODAY'S LESSON WAS SOMETHING LIKE IT..WE LEARNT ABOUT SLOPES AND AVERAGE RATE OF CHANGE IN A GRAPH..THIS WIL BE MORE LIKE A REPEAT TO YOU..BUT I HAVE TO LIST IT ANIHOW..LOLZ!!!

TODAY'S IMPORTANT REVIEW ~

SECANT IS A LINE THAT CONNECTS TWO POINTS ON A GRAPH

SLOPE OF A SECANT IS THE GRADIENT OF THE LINE

INDEPENDANT VARIABLES ARE VARIABLES THAT WE CAN CHANGE

DEPENDANT VARIABLES ARE VARIABLES THAT RESPOND TO THE CHANGES IN THE INDEPENDANT VARIABLE

AVERAGE RATE OF CHANGE MEASURES HOW QUICKLY DEPENDANT VARIABLE CHANGES WITH RESPECT TO INDEPENDANT VARIABLE

AVERAGE RATE OF CHANGE = DIFFERENCE IN DEPENDANT VARIABLE OVER DFFERENCE IN INDEPENDANT VARIABLE

My BiRtHdAy!!! :P

YIPPEEEE!!! YEAHHHH!!! TODAY IS MY BIRTHDAY...WONDER HOW MANY OF YOU ALL REALISED IT..HEHEH..I AM IN A VERY GOOD MOOD TODAY..AND ALL LESSONS WAS MORE FUN TO LEARN TODAY..LOL..HAVE HAD A WONDERFUL DAY SO FAR...HOPE IT WILL CONTINUE..SO..LET'S GET ON AS I GOT LOTZ MORE THINGS TO DO 'TODAY'..^^

UNDERSTAND..UNDERSTAND..UNDERSTAND ~

HOW TO IDENTIFY EVEN FUNCTION??
ALL THE EXPONENTS IN THE EQUATION WOULD BE EVEN
THE EQUATION'S GRAPH HAS A LINE SYMMETRY ABOUT x=0
WHEN f(-x) = f(x)

HOW TO IDENTIFY ODD FUNCTION??
ALL THE EXPONENTS IN THE EQUATION WOULD BE ODD
THE EQUATION'S GRAPH HAS A POINT SYMMETRY ABOUT (0,0)
WHEN f(-x) = -f(x)

SO..WHEN f(-x) $\ne$ f(x)and WHEN f(-x) $\ne$ -f(x), THE FUNCTION IS NOT EVEN OR ODD

MONTH OF AUGUST HAS COME ~

HELLO EVERYONE!! I'M BACK AFTER HAVING A WONDERFUL WEEKEND ^^ FEELS SO GREAT TO GET BACK TO COLLEGE AGAIN..HAHA...AND I HAVE TO CONTINUE ABOUT WHAT WE STUDIED IN CLASS AGAIN..HOPE YOU ALL ARE NOT BORED :P SO TODAY'S LESSON IN CLASS WAS VERY MUCH LIKE LAST FRIDAY..WE JUST STUDIED ONE ADDITIONAL THING..INTERVALS IN A GRAPH AND ZERO'S IN A FUNCTION...

LET'S REMEMBER...

WHEN PART OF THE GRAPH IS BELOW THE X-AXIS, THE INTERVAL SIGN WILL BE NEGATIVE
WHEN PART OF THE GRAPH IS ABOVE THE X-AXIS, THE INTERVAL SIGN WILL BE POSITIVE

ZEROS OF ODD ORDER HAPPENS WHEN GRAPH OF A POLYNOMIAL FUNCTION CROSS THE X-AXIS AND CHANGES SIGN/DIRECTION
ZEROS OF EVEN ORDER HAPPENS WHEN GRAPH OF A POLYNOMIAL FUNCTION TOUCHES THE X-AXIS BUT DO NOT CROSS THE X-AXIS

ZEROS IS THE VALUE THAT CAN MAKE A TERM IN A POLYNOMIAL FUNCTION BECOME ZERO

GRAPHIC CALCULATOR!!!!!!!!!!!!!

HAHAHA...WONDERING WHAT I COULD POSSIBLY POST ON A SUNDAY..WHEN THERE'S NO COLLEGE..NO CLASS..AND I'M SUPPOSE TO BE ENJOYING MY HOLIDAY?? HEHEH..JUST THAT I COULDNT RESIST THE TEMPTATION TO POST SOMETHING ON MY BLOG..SO JUST WANNA TELL EVERYONE..DON'T FORGET TO LEARN YOUR GRAPHIC CALCULATOR BY HEART YA..IT WILL HELP A LOT IN ALL THE NEXT LESSONS..I'LL BE BACK TOMORROW..BUBYE!!!

AND....WE COME TO THE END OF OUR WONDERFUL 2ND WEEK ^^

TIME FLIES THAT PAST, ISN'IT??? ANIWAY..I'VE GOT NOTHING MUCH TO WRITE TODAY..YOU'RE WONDERING WHY??? HAHA..BECAUSE TODAY'S LESSON WAS JUST THE SAME AS YESTERDAY..WE JUST DID EXTRA EXERCISES TO ENHANCE OUR UNDERSTANDING OF THIS TOPIC..SO TO MAKE UP FOR MY LITTLE WORDS, I HAVE INCLUDED A VIDEO(NOT THAT I HAVE NEVER POSTED VIDEOS BEFORE..HEHEH) HERE TO EXPLAIN MORE ABOUT TODAY'S LESSON..=.=

At LaSt I CoMe To WhAt We StUdIeD tOdAy!!!

AFTER SO MANY POSTS, AT LAST I CAN WRITE ABOUT WHAT WE STUDIED TODAY..TODAY'S CLASS WAS ABOUT CHARACTERISTICS OF POLYNOMIAL FUNCTIONS...IT WAS SOMETHING TOTALLY NEW..SO WE ALL HAD TO PAY EXTRA ATTENTION IN CLASS..AS I AM KINDA TIRED OF TYPING SINCE JUST NOW, I'LL GET STRAIGHT TO THE POINT ALRIGHT..CHEERS!!

INFO TO KNOW ~

ODD DEGREE FUNCTION WITH POSITIVE LEADING COEFFICIENT :
DOMAIN = ANY VALUE
RANGE = ANY VALUE
END BEHAVIOUR = EXTENDS FROM QUADRANT 3 TO QUADRANT 1
NO. OF ABSOLUTE MAX/MIN POINTS = 0
NO. OF TOTAL LOCAL MIN POINTS = 0
NO. OF TOTAL LOCAL MAX POINTS = n-1
NO. OF X-INTERCEPTS = MIN 1, MAX n

ODD DEGREE FUNCTION WITH NEGATIVE LEADING COEFFICIENT :
DOMAIN = ANY VALUE
RANGE = ANY VALUE
END BEHAVIOUR = EXTENDS FROM QUADRANT 2 TO QUADRANT 4
NO. OF ABSOLUTE MAX/MIN POINTS = 0
NO. OF TOTAL LOCAL MIN POINTS = 0
NO. OF TOTAL LOCAL MAX POINTS = n-1
NO. OF X-INTERCEPTS = MIN 1, MAX n

EVEN DEGREE FUNCTION WITH POSITIVE LEADING COEFFICIENT :
DOMAIN = ANY VALUE
RANGE = VALUES GREATER THAN OR EQUAL TO a(a CAN BE SEEN IN THE GRAPH)
END BEHAVIOUR = EXTENDS FROM QUADRANT 2 TO QUADRANT 1
NO. OF ABSOLUTE MAX/MIN POINTS = 1
NO. OF TOTAL LOCAL MIN POINTS = 1
NO. OF TOTAL LOCAL MAX POINTS = n-1
NO. OF X-INTERCEPTS = MIN 0, MAX n

EVEN DEGREE FUNCTION WITH NEGATIVE LEADING COEFFICIENT :
DOMAIN = ANY VALUE
RANGE = VALUES GREATER THAN OR EQUAL TO a(a CAN BE SEEN IN THE GRAPH)
END BEHAVIOUR = EXTENDS FROM QUADRANT 3 TO QUADRANT 4
NO. OF ABSOLUTE MAX/MIN POINTS = 1
NO. OF TOTAL LOCAL MIN POINTS = 1
NO. OF TOTAL LOCAL MAX POINTS = n-1
NO. OF X-INTERCEPTS = MIN 0, MAX n

LeSsOnS bY dIfFeReNt TeAcHeR :)

YUP..YOU ALL READ MY POST RIGHT..YESTERDAY'S LESSON WAS THOUGHT BY MS. MALAR BECAUSE UNFORTUNATELY MS. JOANNE COULD'NT COME TO CLASS TODAY..SO BASICALLY WE LEARNED ONE MAIN THONG TODAY..FINITE DIFFERENCES..IT WAS NOT THAT HARD BECAUSE WE LEARNT A BIT ABOUT IT LAST WEEK..AND I HAVE ALSO NOTED DOWN SOME INFORMATION ON FINITE DIFFERENCE BEFORE...WE WERE ALSO TAUGHT HOW TO USE GRAPHIC CALCULATOR TO FIND FINITE DIFFERENCE WHICH IS SO MUCH EASIER THAN DOING MANUALLY TRUST ME..HEHEH..AND WE WERE ALSO GIVEN HOMEWORK OF EXPLORING OUR CALCULATORS FUNCTIONS MAINLY LEARNING HOW TO FIND THE VALUES OF AN EQUATION USING JUST A GIVEN TABLE OF X AND Y VALUES...AND IT WAS HARD TO DO IT AT FIRST..WE HAD TO TRY LIKE SO MANY TIMES..BUT ATLAST WE GOT IT..WELL, I DIDNT GET IT REALLY..IT WAS MY FREN WHO GOT IT AND TAUGHT ME HOW TO DO IT XD!!!

SO...IMPORTANT THINGS YESTERDAY ~

EXPONENT OF A TERM IS CALLED n

nTH CONSTANT DIFFERENCE = HIGHEST EXPONENT OF AN EQUATION

SIGN OF CONSTANT FINITE DIFFERENCE = SING OF LEADING COEFFICIENT

LEADING COEFFICIENT = CONSTANT FINITE DIFFERENCE / n!

! = FACTORIAL (EXP : 4! = 4 x 3 x 2 x 1)

3..2..1!!! LeTs BeGiN cHaPtEr 1...

YEAHHH..AT LAST..WE START CHAPTER 1!! DO I SOUND TOO ENTHUSIASTIC??? MAYBE :P SO I'LL JUST COMBINE THE LESSONS WE LEARNED FOR TWO DAYS (25 JULY AND 26 JULY) AS IT IS BOTH ABOUT POWER FUNCTIONS..SO WE LEARNED MANY THINGS TODAY..

THINGS TO REMEMBER ~

EXPONENT OF A POLYNOMIAL FUNCTION MUST BE A POSITIVE WHOLE NUMBER

WHEN THE HIGHEST EXPONENT OF AN EQUATION IS ODD,
DOMAIN = ANY VALUE
RANGE = ANY VALUE
SYMMETRY = POINT (0,0)
END BEHAVIOUR = AS x$\to$$\infty$, y$\to$$\infty$ AS x$\to$-$\infty$, y$\to$-$\infty$

WHEN THE HIGHEST EXPONENT OF AN EQUATION IS EVEN,
DOMAIN = ANY VALUE
RANGE = GREATER OR EQUAL TO ZERO
SYMMETRY = LINE (x=0)
END BEHAVIOUR = AS x$\to$$\infty$, y$\to$$\infty$ AS x$\to$-$\infty$,y$\to$$\infty$

END BEHAVIOUR
EXTENDS FROM QUADRANT 3 TO QUADRANT 1 = ODD EXPONENT, + COEFFICIENT
EXTENDS FROM QUADRANT 2 TO QUADRANT 4 = ODD EXPONENT, - COEFFICIENT
EXTENDS FROM QUADRANT 2 TO QUADRANT 1 = EVEN EXPONENT, + COEFFICIENT
EXTENDS FROM QUADRANT 3 TO QUADRANT 4 = EVEN EXPONENT, - COEFFICIENT

YeAhHh...OnE mOrE tO gO tO eNd PrErEqUiSiTe SkiLls!!!

SO WE COME TO THE END OF OUR FIRST WEEK WITH THE ENDING REVISION OF PREREQUISITE SKILLS..WE DID TRANSFORMATIONS IN CLASS TODAY WHICH WAS ALSO SOMETHING NEW..SO MY NOTES HERE ARE JUST WHAT I COPIED FROM MS.JOANNE'S NOTES IN CLASS..AS IT'S THE BEST..HOPE YOU DON'T MIND MS.JOANNE..HEHE...

THINGS TO NOTE ~

GENERAL FUNCTION : y = - a. f( k(x+b) ) + c

'-' means refection in the x-axis

a$>$1 means vertical stretch of factor a
0$<$a$<$1 means compression of factor a

k$>$1 means horizontal compression of factor 1/k

0$<$k$<$1 means horizontal stretch of factor 1/k

b$>$0 means horizontal shift b units left
b$<$0 means horizontal shift b units right

c$>$0 means vertical shift c units up
c$<$0 means vertical shift c units down

f(-x) means reflection in y-axis (horizontal)
-f(x) means refelction in x-axis (vertical)

PrErEqUiSiTe SkIlLs!!! BuT sOmEtHiNg NeW ???

SO ON 21ST JULY 2011 WE WERE SUPPOSE TO STUDY PERERQUISITE SKILLS WHICH MEANS REFRESHING MINDS ABOUT WHAT WE STUDIED LAST TIME..BUT..........THIS WAS SOMETHING NEW FOR ALL OF US SUPRISINGLY..WE STUDIED ABOUT ABSOLUTE FUNCTIONS AND ABOUT DOMAIN AND RANGE ON THAT DAY...WELL, YOU ALL KNOW WHAT ABSOLUTE FUNCTIONS IS...WHEN YOU REMOVE THE │ │ SIGN FROM AN EQUATION, YOUR VALUE ON THE OTHER SIDE WILL BE BOTH NEGATIVE AND POSITIVE..SO YOU WILL HAVE TWO ANSWERS...SO ITZ THE DOMAIN AND RANGE RANGE PART THAT WAS A BIT NEW TO US..WE ONLY LEARNED THE BASIC IN HIGH SCHOOL..

THINGS TO KNOW...

DOMAIN = VALUES OF X

RANGE = VALUES OF Y

INFINITE SYMBOL = $\infty$

X$\in ℝ$ FOR ALL POLYNOMIALS

WHEN YOU REMOVE THE │ │ SIGN FROM AN EQUATION, YOUR VALUE ON THE OTHER SIDE WILL BE BOTH NEGATIVE AND POSITIVE..SO YOU WILL HAVE TWO ANSWERS

DENOMINATOR OF A FRACTION CANNOT BE ZERO

EXPRESSION UNDER EVEN ROOT IS GRETER OR EQUAL TO ZERO

ODD POWERED ROOTS HAVE NO RESTRICTIONS

NOW LETS EXPLORE OUR FIRST "STUDY" CLASS =.=

SO WHAT WE DID ON 2OTH JULY IS START OUR STUDY LESSONS...BUT WE DID NOT START OUR CHAPTER 1 TOO FAST...MS. JOANNE GAVE US SOME LESSONS ON PREREQUISITE SKILLS...THESE QUESTIONS ARE THE SAME ONES THAT WE STUDIED DURING OUR HIGH SCHOOL.. IT'S MERELY A REPEAT ABOUT THE BASICS OF FUNCTION NOTATION, SLOPE AND Y-INTERCEPT OF A LINE AND EQUATION OF A LINE..AND OHH YES..WE DID LEARN SOMETHING NEW, FINITE DIFFERENCES..MS.JOANNE THOUGHT WE HAD STUDIED ON IT LAST TIME BUT NONE OF US HAD..SO SHE TAUGHT US MORE ON THAT..BUT FNITE DIFFERENCE IS A QUITE SIMPLE EXERCISE TO UNDERSTAND I THINK...

WHAT YOU NEED TO KNOW...

FUNCTION NOTATION ~ LEARN HOW TO SUBSTITUTE VALUES OF X INTO EQUATION

SLOPE AND Y-INTERCEPT OF A LINE ~ REMEMBER THE FORMULA Y=MX+C..AND LEARN TO STATE THE GRADIENT(M) AND Y-INTERCEPT(C) FROM AN EQUATION

EQUATION OF A LINE ~ LEARN TO BUILD AN EQUATION FOR A LINE THAT SATISFIES SETS OF CONDITION GIVEN LIKE SLOPE, X-INTERCEPT, Y-INTERCEPT AND POINTS

FINITE DIFFERENCES ~ LEARN TO DETERMINE FINITE DIFFERENCES USING GRAPHIC CALCULATOR AND MANUAL CALCULATION TO FIND OUT HIGHEST EXPONENT OF AN EQUATION AND THE SIGN OF THE LEADING COEFFICIENT...SO IF GET THE 1ST FINITE DIFFERENCE(FD)- LINEAR EQUATION, 2ND FD - QUADRATIC EQUATION, 3RD FD - CUBIC FUNCTION, 4TH FD - QUARTIC FUNCTION, 5TH FD - QUINTIC FUNCTION...AND SO ON

LeT's StArT wItH oUr LeSsOnS!!! ^^

OOPS!! THAT SOUNDS SO LIKE A TEACHER :P LET'S CHANGE IT THEN..HMMM..HMMM..GOT IT!! LET'S EXPLORE OUR FIRST LESSON TOGETHER!! ^^ THIS BLOG IS ABOUT CHAPTER 1 ADVANCED FUNCTION : POLYNOMIAL FUNCTIONS..OH WAIT..I FORGOT..WE DID NOT STUDY ANY ADVANCED FUNCTIONS ON OUR FIRST DAY..OUR FIRST DAY WAS A FUN EXPERINCE OF GETTING TOO KNOW OUR NEW FRENZ AND TEACHERZ.. I REMEMBER WE HAD AN ICE BREAKING SESSION ON THAT DAY..EACH US WERE ASKED TO STICK A PAPER ON OUR BACK AND INTRODUCE OURSELVES TO OUR NEW FRIENDS AND THEY WILL HAVE TO WRITE ON THE PAPER ABOUT THEIR FIRST IMPRESSION ON US..IT WAS REALLY INTERESTING TO SEE ALL THE WORDS OF WHAT OTHERS THINK OF US..BUT I DON'T WANT TO TELL HERE WHAT WORDS I GOT..HEHEH..WE EVEN WROTE SOMETHING ON MS.JOANNE'S PAPER TOO XD!!! WELL, TATZ MORE TO THE FUN PART..WE WERE ALSO GIVEN SOME INFORMATION REGARDING OUR SUBJECT BY MS.JOANNE..70% OF OUR ASSESMENT MARKS WILL BE COUNTED THROUGH QUIZ, TESTS, PROJECTS AND ASSIGNMENTS WE WILL HAVE TO DO..NOT MUCH THOUGHT TO GIVEN TO IT THEN..BUT KNOW WE REALISE HOW IMPORTANT IS IT TO DO ALL OUR ASSIGNMENTS (LIKE WHAT I AM DOING NOW..HAHA) ^^

WhAt We WeRe TaUgHt By Our aWeSoMe TeAcHeRz In OnE wEeK ???

HEHE..YOUR THINKING WHY I SAID "TEACHERZ" INSTEAD OF "TEACHER"..WELL, WE ARE LUCKY ENOUGH TO HAVE NOT JUST ONE TEACHER BUT TWO TEACHERZ WHO ARE GUIDING US IN OUR ADVANCED FUNCTION CLASS..MS. JOANNE AND MS. MALAR..YEAHH!! BUT IT'S MAINLY MS. JOANNE THAT TEACHES US EVERYDAY ^^ SO AS YOU KNOW, I STARTED THIS BLOG ONLY YESTERDAY...NEVERTHELESS WE STARTED LESSON LAST WEEK..SO I AM GONNA HAVE TO TELL YOU ALL WHAT WE LEARNED THROUGHOUT THE PAST WEEK...WELL, TO MAKE IT EASIER I WILL POST WHAT WE LEARNT ACCORDING TO EACH CLASS ALRIGHT??? OKAY..HAVE FUN READING IT!! XD =.=

AfTeR oNe WeEk In ClAsS...

YEAHHHH!!! THAT FAST TIME FLIES..IT SEEMS JUST LIKE YESTERDAY THAT I REGISTERED IN FOR THIS PROGRAMME..BUT YET ONE WEEK HAS GONE PAST..AND IT WAS NOT A LIGHTWEEK FOR ALL OF US..WE HAVE ALREADY STARTED LEARNING AND THERE'S HOMEWORK EVERYDAY..AND WE HAVE NOW GOTTEN OUR FIRST ASSIGNMENT FOR THE SEMESTER...WHICH BRINGS ME TO THIS VERY BLOG..I'M GONNA HAVE TO MAKE THIS BLOG AS AN E-JOURNAL FOR THE CHAPTER 1 ADVANCED FUNCTION..SOME MIGHT FIND THIS ADDITIONAL HOMEWORK BURDENING..WELL, YEAH..WHAT WITH THE ASSIGNMENTS OF ALL OTHER SUBJECTS..BUT I THINK THIS ONE ASSIGNMENT THAT I HAVE GOT IS SO FAR THE BEST!! "CREATING A BLOG!!!" HOW COOL IS THAT..VERY~ AND EVEN MORE FOR THOSE LIKE ME WHO ARE CREATING A BLOG FOR THE FIRST TIME..ITZ LIKE EXPLORING SOMETHING NEW :) NOW THAT I HAVE EXPLORED IT A BIT, I WILL BE STARTING TO POST SOME COMMENTS, IMAGES AND VIDEOS IN THIS BLOG TODAY..SO TO ALL MY FRIENDS WHO VISIT MY BLOG..HOPE YOU ALL WILL FIND THE INFORMATION HERE USEFUL YA!! AND PLEASE POST ANY COMMENTS IF YOU WOULD LIKE TO SAY SOMETHING ABOUT BY BLOG..THANKZZ!!! ^^

FiRsT tImE bLoGgEr??? Oh NoOoOoOoOo!!!

HaHaHa..JuZ kIdDiNg!!!

WeLcOmE eVeRyOnE ^^