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Review of Functions - Lt 1.31 Lil 1.5 La"mm.or m Tm...

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Unformatted text preview: Lt, 1.31 Lil] 1.5, La "mm .or m Tm;- FORUM» A = 'zrr‘z F0)? 7715 0:751? a): :9 chLE IS A RULE wHICM 19550049735 WIT” EBCH P0677105 REHL NUDBER I" EXfiCTL‘i om: omen NUDBEI? F)’ NfiI'IELy) THE MEI? or n CIRCLE OF mamas r, H REfiL-VflLUED FUNCTION 0F fl 8531.. VfiflIBBLE ( 0R JUST FUNCTMIU p—u—n—n— Fol? SHORT) cow’s-rs or Two mmsg: u) A SET D 0F R891. NUDBERS CfiLLED THE Darwin) w.) n RULE wmcfi 935000155 mm EVERY 8513).. NUUBER x "u THE Donaw D EXDCTLY ONE nunersn y craLLea "WE VALUE OF THE FUNCTION AT 7L. Tiff SET OF flu. vfiLuEs OF 7715 FUNCTION (5 cfiLLED ITS Rimes _ THE RULES flRE GENERfiLL)’ GWEN NHnES LIKE ptg, “'! F363". IF rm: Nana IS P, ms» ms VALUE 0; P m x :5 orrsm wmrmu ch) L "PoF at") 891195)? Wm)! : y : ch) SonE SPECIBL Fumcnmvs HfiVE NBflES RESERVED FOR THE”) E. 6., sm , cos, , In, 2.173).", swim)“, sons new»; or DESCRIBING FUNCTIONS : .‘L . FORUULHS 5.6., Pox) = “XL IN THIS 0955 TM“ Donmm IS GENEIi'auy THKEN TO BE THE NfiTURBL Donnw , 125., THE Lfificfisr 557 OF REHL munBERS x To wmcH ms Fannum cam BE flPPuED To owe Amman msm. wanes/z. FOR Fm = W33??- ms wow) 86' ~14x41. EXCEP'noN: THE Fokflum nfiy ARISE w Sane cpmmxr mm PLBCES FURTHER RESTRICTIONS am 1775 Donemv, E. c. , z ,9 = 1rr makes PERFECT SENSE FOR P f o, 307 CIRCLE; Do NOT mews $UCH may”, A Few srecnm. 01.19555; 0F Fumcnows vsscmgsv By FDRDULBS : 5. Powen Fumcnoms : x 3 3 x‘ (= (1/3?) ) 3 43! L = 1/3 x ) -14 X xv .1; PoLYNanmLs : 5x + 3 xl-ax +1 6x3-7 8 ‘qu- §x3+7xl+ 5x -.2 l anx +q" x +---+qzx “1.x +a° RfiTIoNfiL FDNCTIo/vs : 5X * 3 ...__.._-— (011635 Fax) 19m) QCX) IM’E POLYMOUIBLS' V y: x7" «I . GRHPHS c PHRHBDLF) ) fiLL FUNCTIONS HfiVE GRDPHS’ E. 6., x Y , .L - x L ( HYPERBOLH ) X ETC, N . on THE OTHER 029nm, Hwy cunuE IN THE xy-PLHNE “mar P195555 7'»: “ vEfiTlcm. LINE TEsT " DEFINES A FUNCTION wh‘OSE vmuE HT 7: 15 m5 HEIGHT 0F me CURVE neouE (0R BELow) X , Y «no-c BHNGE u.--- t l O i I DOHBM) 3. GEOHETRICHLL)’ F0)? ExnnPLE , cas x fier 5:» x ME DEFINED By THE PICTURE (Cosx, Sm x) gm ) '1 = 38C LENGTH ( CLOCKMSE CIRCLE or: w; >5 RHDIDS 1 ”BOUT mm; m IF )C‘ O ) THE 08mm} f (50) / THEN THE REST: 1 Sin - ._._.—— hmx: x SECX' rosx COS X I aal’x-t Cosx CSCX~ smx SODE SPECIBL VBLUES YOU DUST KNOW 3 51» X o if if- ? I o - 1 cos x I £5. £1. .1; a 4 o 5005 IDENTITIES you DUST KNOW : cosax + Sma‘x = I I + hm‘x = sectx swlx = 9.5m x Cos x z 2. caslx = cos X-SINX coszx = fLH Cos-1x) sm"x 7— tcl- Cos-IX) HERE '5 ANOTHER (seemmmy coo, Bur vsny mponmmr ) csonemcm way or DEFINING FUNCTIONS: SUPPOSE pm) >, 0 on) sane INTERVBL I mvo FIX sons 6:. no I. In. .c-.-l ‘ Fan [my x W 1' DEFINE anal) UNDER y=pcx) Man a To x , :F X 3" a. FLY.) : ~ muss uwosn y=flcx2 mm x Tea 1" X‘OL 3 5.6. sPEcmL c955 : wE lulu. SEE LBTER “rm-)7 m5 “ PROPER " DEFImmom 0F ms anm Losnmmn Fumcnom In x, FDR x >0, IS As 7775 " ARE/9 Fumcnon" F0}; ch J = '5‘; on) (age) wm-I a: l [9850 = In X X flu. or me "usum." PROPERTIES or we NBTUIML Loefimrfin c come» you nusr «mow ) cmv BE PROVED Fkon 'nm DEFINITION : Y y:’nx ..... x (In) In (I) = 0 had”: Ina-Link a . |n(-'-°- : Ink-Ink I" lnLa ) = rlna. H, fiPPLlCH TIONS 909an I A SOUP conpnmy wmv'rs TD DBNUFACTURE A Tm com (N THE snaps OF A man czxcuLnR cyLwDER ( [j ) war 3 mm. How 500 an 0F souP, EXPRESS THE 1900va OF Tm REQUIRED TO BUILD THE 019m 35 a FUNCTIoN 0F THE Ramos r OF THE CBN L nwo THINK 313007 77-h? PROBLEn 0F mema n 0001625 or r' Th‘fiT wru. mMmtE THE finovm' 0F nHTEmFJL REQUIRED ). ll 1 1. SURFACE HPEI? )9 m MW 4- .2er B = .211'rz+ .2er h 500 voLunE : 500 = m3}, .1; I, = ~53- ; $00 Aer) = .211? +.21rr~(-——-w,_) ’9 THE any?” 0F 19m Looks noocmv ms rms A ' r \ THIS vfiLuE 0F 1‘ www Remake THE 1.59:7" 1900va OF TIN. WE («ALL Fwo rr LflTER. 5'. INVERSES fl Fumcnom P wmi 00mm) D IS smo 12: BE ONE-[q-oms om D n: ms GRfiPfl passes ms " Homzommz. LINE rssr ". 7 Y ONE — TO - ONE Ivor omE-TD— ONE IF P (S ems-To-oms, mm we emu DEFINE mvomE/e FUNCTION, -' ; wmrrsro P awn CflLLED m5 mvERSE 0F F 2:11:04 "umooss,' fl : 3 5.6., IF Pa) = X om (-°°,°°), WM F a) = Vx BECfiUSE .v 3 p(pLX)) '-' F (X3) : 1/ x3 z X. MIDPORTHNT EXBDPLE : PLX) : '0 X on) (o’eo) Y THERE IS IUD SIDPLE FORDULH FOR THE on INVERSE In 0F In J BUT IT my; 3 “,0; warns BNO B synom. (scrutiny) Two synBoLS ) -I In :5 crmeo T7125 expomsmrm FUNCTION nmo n5 vmus flT any x w (Jena) :5 wmrrrsn exp (X) 0R X 8 GRfiPfis 0F vaRsE FUNCTIONS fiRE 037‘me BY " BEFLECTWG ACROSS TH‘E LINE )1 = )C ' $0 y:cx x SINCE lnx fin») e ans wususss, In): a :X O<XL°O ) ln(e")=x -°°‘X<°° ’ THE PROPER'UES OF In x LISTED EBRUER mnwsmrc‘ mm Tms FfinILmR PROPERTIES OF THE EXPDNENTML FUNCTION ( tome» You HOST Imam) : [4 Fumcnoms WI 1317:" mm amE-To—omE on “me”? ENTIRE Dormws OFTEN BEconE ONE-Ta—ONE wHEm THEIR Donmros HIRE RESTRICTED 50 mEy fiflVE INVERSES ON THESE RESTRICTED DODHINS, EXfinPLES : 3, y: smx on) [“3395] 4 y : 5w x = arcsw x on [1:] I! THE "moms ' no [-15 .E wHoSE same as X ( no 5mm? FORDULH FOR ConPuTms Tms one ) H. y:cvs X on [0,173 -l y = (‘05 x = Arccosx on) i-UJJ - THE "mums" m [0,173 wHosE caSmE 13 x 5. y=¥n~x mo (—7"? III) 1.0:. -I y: 759“) Y =fircz'mo X 0N C'wam) = THE “ANGLE"W (-51%) wHOSE 779N65NT '5 X (N0 smns Fonnum FDR ConPumua 771/5 one ) ONE on» Do sonETmNG 81mm)? FDR cor X , 55c x BM) c5c x BUT WE WILL HfivE PELHTIDEL)’ LITTLE USE FOR THESE ...
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