0 x < 5 PIECEWISE FUNCTIONS DAY1 4.7
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1 PIECEWISE FUNCTIONS DAY 7 GOAL Red fuctios of grphs represeted by more th oe equtio fuctios of grphs represeted by more th oe equtio Grph piecewise fuctios PIECEWISE FUNCTION A fuctio defied by two or more equtios Ech piece of fuctio hs differet prt of its domi F(X) = X, if x 0 X +, if x > 0 Whe x 0 Whe x > 0 X Y = X- X Y = X DOMAIN: RANGE: - - EVALUATING A PIECEWISE FUNCTION F(X) = X, if X +, if x 0 x > 0 Evlute fuctio f bove whe () X = 0 d (b) X = Whe X = 0 F(X) = X - Whe X = F(X)=X + F(0) = F() = F(X) = -X X x < 0 0 x < 5 Evlute fuctio f bove whe () X = 0 d (b) X = Whe X = 0 F(X) = Whe X = - F(X) = F(0) = F(-) =
2 WRITING A PIECEWISE FUNCTION Explortio pg 7 equtio tht represets vlues of Fuctio whe x 0 Equtio Domi equtio tht represets vlues of Fuctio whe x > Equtio Domi - GROUP WORK: WRITE PIECEWISE FUNCTIONS #9 pg 9 equtio tht represets vlues of Fuctio whe Equtio Domi equtio tht represets vlues of Fuctio whe Equtio Domi - # pg 9 equtio tht represets vlues of Fuctio whe Equtio Domi equtio tht represets vlues of Fuctio whe Equtio Domi equtio tht represets vlues of Fuctio whe Equtio Domi CW#7; 7 Worksheet; #,5 HW#7 pg, 9,,, 5, 7
3 PIECEWISE FUNCTIONS DAY 7 PIECEWISE FUNCTION A fuctio defied by two or more equtios Ech piece of fuctio hs differet prt of its domi F(X) = X, if x 0 X +, if x > 0 Whe x 0 Whe x > 0 X Y = X- X Y = X DOMAIN: RANGE: - - GRAPHING A PIECEWISE FUNCTION F(X) = -X if X if 5 x < 0 x 0 Whe 5 x < 0 Whe x 0 X Y = -X- X Y = X (strt with ENDPOINTS OF EACH PIECE) DOMAIN: RANGE: -
4 GROUP WORK: To grph strt with edpoits of ech piece F(X) = if X + if X if x < x 5 x > 5 Whe x < Whe x 5 Whe x > 5 X Y = X Y = X+ X Y=X DOMAIN RANGE Grph fuctio below F(X) = -X X x < 0 0 x < Whe Whe X Y = X Y = DOMAIN RANGE Worksheet 7, pg 9, - / HW# pg #5, 7, 9
5 ARITHMETIC SEQUENCES PIECEWISE FUNCTION A fuctio defied by two or more equtios Ech piece of fuctio hs differet prt of its domi WARM UP Evlute fuctio F(X) = if X + if X if x < x 5 x > 5 F(-) = b F() = Grph fuctio bove STEP: Grph F(X) = STEP: Grph F(X) = X + STEP: Grph F(X) = X x < x 5 x >
6 Lesso terms of Ler rithmetic sequeces Wht You Will Grph rithmetic sequeces Arithmetic Sequeces terms sequeces of rithmetic sequeces rithmetic s fuctios bullrryarithmetice bulry SEQUENCE Grph rithmetic sequeces 0 Writig Terms of Arithmetic Sequeces rithmetic sequeces s fuctios SEQUENCE: A ordered list of umbers A sequece is ordered list of umbers Ech umber i sequece is clled term Essetil Ech Questio How c you use rithmetic sequece to term Ech hs specifi c positio isequece sequece umber i is term quece, p 0 erece, p 0 describe Terms of Arithmetic Sequeces Writig ptter? 5,, 5, 0, 5,,, Observtio of umbers Ech umber i sequece is clled term A sequece sequeceisis ordered ordered list list of umbers i which differece 0A rithmetic orm i Ech term hs specifi c positio 5 positio sme th terms, orrd umbers i sequece list, is 0 betwee ech pir of cosecutive st positio positio tio 5,, 5, 0, 5,,, Ptter Core Describig Cocept st positio rd positio th positio Work with prter Use Sequece figures to complete tble Plot poits give Arithmetic by your completed I tble Describe ptter of y-vlues ARITHMETIC SEQUENCE: A Sequece with Costt Differece Terms rithmetic sequece, differece betwee ech pir of cosecutivebetwee terms Core Cocept differece is clled differece y Ech term is foud is= sme This = = commo = 5 by ddig 0 Observtio (N) commo differece to previous term = Arithmetic5,Sequece, 5, 0, 50 Terms of rithmetic sequece I rithmetic sequece, differece betwee 0 ech pir of cosecutive terms commo differece is sme This differece is clled commo0differece Ech term is foud ( ) is series by ddig commo differece to previous0 term t idictes GOAL: terms of Arithmetic o sequece sequece) 0, Terms of poits rithmetic (get, 5, 5 Sequece of strs, 5, ol omissio Grph Arithmetic Sequeces Extedig Arithmetic Sequece 0 tio I 0 5 commo differece of sides, y fuctio(equtio) of Arithmetic Sequece ics, ext three terms of rithmetic sequece mes eries d so Use Equtio to fid distt term, ie 0th term of sequece es ellipsis idictes y b = 7, =,,, = = =5 re more terms io EXPLORATION: A PARTNER uece tht re SOLUTIONWORK WITH Extedig Arithmetic Sequece NG 5 Use tble to orgize terms d fid ptter Use to complete rithmetic tble figures ext three terms of sequece d so Positio poits give by dictes Plot 7,,,, completed tble of 5 term iswith completed ptter equtio terms Describe Ech 7 less th Term Y 7vlues previous term So, re SOLUTION of circles, y 0 commo differece 0is 7 +( 7) +( 7) +( 7) 5 Observtio (N) Use tble to orgize terms d fid ptter Add 7 to term to fid ext term y = = = =5 c = Positio 5 7 Positio TermTerm ( 7) +( 7) +( 7) +( 7) +( 7) previous term So, +( 7) commo differece is 7 three 5,, d 9 Add 7 The to ext term toterms fidre ext term of rows, Positio Moitorig Progress Term of dots, y 7 Ech term is 7 less th Help i Eglish d Spish t BigIdesMthcom 5 ext three terms of rithmetic sequece 9 Which vrible is grphed o X AXIS? +( 7) Which +( 7) vrible +( 7) is grphed o Y AXIS?, 0,,, 0, 0,,,,,,, Commuicte Your The ext three Aswer terms re 5,, d 9 FIND ITS EQUATION Y = clier you use rithmetic sequece to describe ptter? Give exmple pter How Writig Fuctios from rel life Moitorig Progress Help i Eglish d Spish t BigIdesMthcom CAN I chemistry, wter is HO becuse ech molecule of wter hs two YOU THINK OFclled AN ALTERNATE WAY TO GET THE EQUATION? d ext terms rithmetic sequece hydroge toms oethree oxyge tomofdescribe ptter show below Use ptter to determie umber of toms i molecules, 0,,, 0, 0,,, = = = = =5,,,,
7 EXTENDING AN ARITHMETIC SEQUENCE Wht re ext three terms: -7, -, -, -,,, -, 0,,,,, GRAPHING AN ARITHMETIC SEQUENCE Observtio (N) Term (A ) WHAT VARIABLE GOES ON THE X AXIS? WHAT VARIABLE GOES ON THE Y AXIS? WHAT IS THE EQUATION? WHAT WOULD BE AN ALTERNATE WAY TO GET THE EQUATION? Observtio (N) Term (A ) IDENTIFYING AN ARITHMETIC SEQUENCE FROM A GRAPH STEP : Mke Tble of Vlues STEP : Determie if re is Commo Differece betwee A terms (Y vlues)? X Y 0 0 (, 5) (, ) (, 9) (, ) 5 7 IS THIS AN ARITHMETIC SEQUENCE? WHY YES OR NO?
8 WRITING ARITHMETIC SEQUENCES Observtio (N) Term (A ) 7 Commo Differece (D) EQUATION A = First Term + Commo Differece (N ) A N = A + D (N ) EQUATION SIMPLIFY WHAT WILL BE THE 50 Th term? A 50 = GROUP WORK: WRITE AN EQUATION FOR ARITHMETIC SEQUENCE,,,, OBSERVATION (N) TERM (A ) COMMON DIFFERENCE (D) = EQUATION A = First Term + Commo Differece (N ) A = + (N ) SIMPLIFY A N = WHAT WILL BE THE 50 Th term? A 50 = WRITE AN EQUATION FOR ARITHMETIC SEQUENCE, 0, -, -, OBSERVATION (N) TERM (A ) COMMON DIFFERENCE (D) = EQUATION A = + (N ) SIMPLFY A N = A 50 = HW#, pg, -5od, 9-7 odd, d 5 (START IN CLASS)
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