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MATH 105 TI83 Plus Graphing Calculator Tasks I Graphing Functions Enter the functinn intn the ealeulatnr Press Iou Plotz not I Type in the funetaon and press For the rndependent vanabie use x whreh is entered using th key xxxxxx Graphthe functinn To graph and make sure your graphm sereen displays the standard windowquot in whreh x and y both range from e10to 10 press and choose optron 6ZStzrdzrd Kyoujustpress the function will appear in the last Window the eaieuiatorused window size 11 Special Functions Ahsnlute Value runeu39m Ixi Press the Press mto hrghhght the NUM menu and choose opuon1zbs This Don39tforget to close the parentheses Greatest Integer functinn step funetaon re P s mto hrghhght the NUM menu and choose opaon 5 m This pastes Int rnto the sereen and you ean type in the rest othe variables Don39tforgetto close the parentheses Piecewise Defined functinns This rsbestexpiatnedbyanexarnpie To enter mm pm pm y 2r 1rlt1 dothemlowmg 39VIE3X1Xlt1 Wear Xigtltz1 TEST ehoose TEST onneetrng the two preees othe graph ls e ms lecelsnm enotthe m h not really part ofthe graph It ls afeature p g olots even when rtrs not supposeolto The real graph would look llke thrs Kyou haye afunctlon x and wlsh to evaluate the functlon for eertatn yalues ofx you ean enter the funeuon rnto your ealeulator and have rt eyaluate for you e rnolependentyarrable use x whlch ls functlon rnto Yt There are two ways to Press Type ln the functlon and pres Forth entereol uslng th key Assume you entereol the evaluate the functlon Method 1 Press then m to hlghllghtYrVARS anol ehoose opuon 1 Funct Ion Then ehoose optron 1 Y1 Thls pastes Y1 rnto the horne sereen Then type ln then the Xvalue you want andthen Press Method2 Graph the functlon pres and ehoose o tron1vzlue Atthe bottom CALC ofthe graph you wlll seex Type ln the number and press Enter the function rnto Yt Pres TBLSET dlsplay 1Tb ls the rnerernent for x 50 lf Tbl Start rs0andTbI 05the XvalueswlllbeO 5 TFIBLE SETUP 1 15 ete lfyou ehoose Auto the table wlll be TblStartB generateol autornatreally lf you ehooseAsk the 4T 1 ealeulator wlll ask you to type ln the x yalue lt ix x m e if anI have any data in ymlr lists key then ehoose optxon1Edlt e1ear that u t t p 2 see step 3 2 Clear ynnr lists if necessary ey then ehoose optron4 Cl rL I st When 0 IrLI st appears on the sereen n the L1 key Pres Ifyou ke ey the have more than one hstto e1ear hen Cl rL I st appears sereen press th y then the L1 key then the eornrna key then the key then the L2 key ete Pres ta ress e key then ehoose optron 1 Ed It Enter your data by typrng m the numbers and usmg the arrow keys 4 Make a seatterplnt nrynnr data then STAT PLOT All the Plots shouldbe Tum P 101 0n Choose optaon 1 P 101 Use the arrow keys to hrghhght the wordOn and rnake sure the sereen looks hke thrs Press This needs tn he dune nne time nnly Pre TALOG and use the down arrow key to move down until D Izgnost d seleeted Press Thtspastes thgnostu mnto the home sereen Press eoef etents 5 Find the enrrelatinn ene ieient and the regressinn line en LC Press use the arrow key to move to CA Choose optron InRegzxb L InRegzxb appears on the math sereen Press 6 CubicReg 7 QuartReg 5 Fur future use the regressinn line can he saved as aruneu39nn Pr r etthur ntth t Rrrsr toEQ Now ehoose opuon 1 RegEQ The regressron equatron rs enteredrn as a Yvalue 7 Flat the regresshrn une Lhrnllgh the paints Press the button a Return ynllr eahulatur hack to nnrmal graph made off all Plots see Step 4 but turn plots orrrnstead of On Return to the standard wrndow hen ehoosrng opuon 6 ZStzndzrd Tum by pressrng 9 Predict snmevalllesllsing theregresshrn line your data do not extrapolate Pres e the arrow key to move overtoYrVARS ehoose opuon 1 Funct ton then ehoose the P value forwhxeh you enteredthe regessron equatron Press the key the xvalue you want andthen the key Press V Solving EquationsFinding Zeros of Functions Kyou have an equatron rewnte rtrn the formr r th 0 Press Type m the funetronr and se x whlch ls entereol uslng the key Graph ero pres e molepenolent vanable the funeuon pres CALC and ehoose optron 2 z a The ealeulatorwrll askyou to move the eursor to the left V 2 5 ofwhere the zero ls Use the left and ng tarrow keys to move to the lelt ofwhere your zero ls on the graph ther rntereept Press Left Round 0 You are now askeolto move the eursorto the nght of WWW15 where the zero ls Use the nght arrow key to move to the nght of where your zero ls on the graph the x rntereept Press You are now askeoltomove the eursor elose to where the WM zero ls Use the left arrow key to move elose to where yourzero ls on the graph the rrntereept Press You wlll now get a declmal apprommauon ofyour answer 3572355 In all of these lelt andnght othe rntereept you ean save trme by slmply typrng m a number For example when you are asked for alelt boundln the above example just for Impnrtant nnte nn snlving equatinns Occaslonally you may get an answer sueh as 4 49999995 You ean be reasonably cenaln the answerls e1 5 Also keep m mlnolthat a ealeulator answer on 3333333 ls really 2 or If make Knot the a tan r u m al ra l nuul r mall r wmdow Dolng thls vvlll ensure thatyou see all ofthe zeros You vvlll needto ndthem all VI Finding Points of Intersection of Curves functlon x r gx m nlat r ano raphthern rnterseeaon ls m the vlewmg wlndow and then press CALC and ehoose opaon 5 Intersect v wax15 You Will be asked whleh eurye you want to use as the rst nons graphed Kyou only have two euryes grapheol press to aeeept the defaultflrst eurye 15 seeonol eurye thls lsJustln ease you have more than two funetlons raphed Ifyou only have two euryes graphe press 139125532 J 6 The eornrnents ln the Imp nrtant nnte nn snlving equz nns also apply herel a Nentyou are askeolto rnoye the eursor nearthe po lnterseeaon Use the arrow keys to do so and pres You answerwlll appear 1st532 VI Finding Maxima and Minima decreaslng or ylee yersa In addmon ths relates to fdeng the range of a functlon you have a functlon x press lnolependentyanable use x whlch ls entereol uslng th Type In the functlon x and press For the ke Graph the functlon rnake CALC anolehoose opaon 3mlnlmun or4 mlemum From here on frndsng zeros m m v V n annrtant nnte nn snlving equatinns also apply herel MATH 105 TI 5 Graphing Calculator Tasks I Graphing Functions Enter the runeu39nn intn the ealeulatnr Press andthen oryx Type m the funetaon and press use x whreh rs enteredusrng the For the rndependent vanable key Graphtheruneu39nn To graph and make sure your graphmg sereen dsplays the standard wrndowquot m whreh x and y b 3 for ZOOM andt en or D Kyoujustpress appear m the last wrnddw the ea1eu1ator used or p V wd h ddfferent wmdow srze 11 Special Functions Ahsnlute Value funcdnn then MATH rr tttr abs Thrs pastes bars Don39tforgettduseuneparenuneses Greatest Integer runetinn step funetaon Press andthen or x then MATH Pres or UM andchoo nt Thrs pastes wt rnto the sereen and you ean type m the rest othe vanables Don39tforgetto use the parentheses Piecewise De ned functinns 3x71xlt1 Thrsrsbestexplarnedbyanexarnple To enterye ZHSJZI doLhefollowmg oryxthentypem3gt391x 12x5x EST The sereen looks hke thrs 35 Mme to see the graph Yhspleue ts Nov pen otthe gmph graph Itrs afeature ofthe ealeulatorthat it tries to eonneet the olots even when it is not supposeolto 1 The real graph would look llke this 111 Evaluating Functions Kyou have afuneuonr and wlsh to evaluate the funeuon for eertarn values ofx you ean enter the funeuon into your ealeulator and have it evaluate foryou orym Type in the functlon anol dofone level ofthe rnenu Now EVAL Typernthexvalueyou vvant anol press IV Plotting Points and Finding Regression Curves e irynu have any dztzi key then ehoose opuon Ifthe narnes xStat and yStat are aeeeptable to you pres tvnee elear thatu t Knot begm entenng your data see 3 2 Clear ynur lists it necessary Alter eornpleung Step 1 press 3 Enter ynur data Enter your data by typrng m the numbers and usmg the arrow keys Enter the data m x y pans 4 Make a seatterplnt nr ynur data c1ear any funeuons that are present ANGE Selecnhe x Pr then ear on the sereen You ean em ess the DRAW and y ranges that wru rnake your data app quotsomz The a and b form the regressron equauon y abx The eonelatron eoemerent rs on r r 7u7ro2 95 7 5 mm the regressinn ne the y1 then was then ress STAT and use the arrow keys untu the tnang1e rs next to Reg Eq Seleet Reg Eq by pressrng The regressron equataon rs enteredrn as a 5322 y alue Now pres M5 GRAPH Ifthe pornts do not show up 2 7 Predict same values using the regressinn une Make sure the ya1ues you want to plug m for x are between the hrghestand1owestrva1ues ofyour data do not extrapolate Press e d e oose EVAL Enter the xvalue you want 8 Return your calculator back to normal graph mode Return to the standard window by pressing then ZOOM then choosing ZST D V Solving EquationsFinding Zeros of Functions If you have an equation rewrite it in the form x 0 Press and then for y X 2 Type in the function x and press Graph the function by pressing M5 make sure the x intercept is in the viewing window and then press MATH and press for ROOT Use E or E to move the cursor close to the x intercept and press Important note on solving equations Occasionally you may get an answer such as 1 49 9 9 9 9 9 5 You can be reasonably certain the answer is 1 5 Also keep in mind that a calculator answer of 2 3333333 is really 2 or If you get a decimal answer for which you do not recognize the rational number equivalent make sure your instructor allows an approximate answer for the problem If not you will need to nd the exact answer using algebra Also make sure you look at the graph in a larger and or smaller window Doing this will ensure that you see all of the zeros You will need to nd them all VI Finding Points of Intersection of Curves If you want to nd where the graphs of x and gx meet one option is to nd the zeros of the function x gx Altemately you can enter f and g into your calculator and graph them After they are graphed and the point of intersection is in the viewing window press MATH and press then I S E CT Use E or E to get the cursor on the rst graph Press ENTER The cursor jumps to the next graph If this is the incorrect graph use E or E to get the cursor on the graph you want Next use E or E to move the cursor near the point of intersection and press ENTER The answer appears The comments in the Important note on solving equations also apply here VI Finding Maxima and Minima This also relates to nding where a function is increasing and where it is decreasing because the locations of the maXimaminima are the places where the function changes from increasing to decreasing or Vice versa In addition you can use this to nd the range of a function If you have a function x press GRAPH and then for y X 2 Type in the function x and press Graph the function by pressing M5 make sure the maximumminimum you want to find is in the Viewing window and then press MATH and again Now press either FM I N or FMAX From here this works just like section V on finding zeros Use E or E to move the cursor close to the maximumminimum and press ENTER The comments in the Important note on solving equations also apply here MATH 105 TI8992 Plus Graphing Calculator Tasks I Graphing Functions zaa nzert al39lste le L39i39 Press El H ype tn the funeaon and press For the lndependentyanable use x Thls ean also be done from the home sereen uslng 1 De ne andthentyplng y1xandthe funetlon deflnltaon Press Graphthe functinn T graph and make sure your graphmg sereen dlsplays the standard Wlndowquot m whleh x and y both range from 71 to 1m ress Zoom and then oomstd Ifyoujust press EIGRAPH the funetaon wlll appearln the last Wlndow the ealeulatorused or on only see part h r wlndow slze 11 Special Functions Ahsnlute Value l39uneljnn Pres 39quot lt m tl nr VTH then ATM and choose 1 Number andthen 2 abs Type ln whatgoes mslde the absolute value symbols and don39tforget to close the parenth es Greatest Integer runetlnn step funeaon Press El H then type 1 nt x for the greatestlnteger funetlon ofx Alternately press El v t e MATH and choose 1 Nu r and then 41Part Type ln whatgoes lnslde and don39t forget to close the parentheses Piecewise De ned Functinns Thls ls best explamed by an example To enter 3X4 K1 mm n y WWW T 2X5Vx21 do the followlng I ve then type lnto yl the funeaon 3x71 k m mb 1 t called when quot andthen x a 1 For yz type 2x5 E 1 Press El GRAPH to see the graph y 111 Evaluating Functions you have afuneuonr and wish to evaluate the funeuon for eertarn values ofx you ean enter the funeuon into your ealeulator and have it evaluate foryou From the horne sereen pres 1 Define andthentype t x and the funeuon de nition Press Next type f 5 or whatever value for x you want and press Enter the funeuon into yl Press El TblSet Use to ehange the settings tol start is the first value for x that you wish to display htoi is the inerernent for x 50 rttol Start is m and um M B5Lhexva1ueswlllbe l 15ete Graph lfyou ehoose AUTO the table Will be generated autornaueally lfyou ehoose ASK the ealeulator will ask you to typ in the x value Press to save this lnfol39ma n onee you are done setting up the table press El TABLE IV Plotting Points and Finding Regression Curves 1 Enter ynllr data values Press El HOME to rr sereen Press M t i x Edi to r Next ehoose 3 New Make sure Typers set to Data and Folderrs set to midi n In the Variable box type avanable name for example stat and press Press ag and you see the DataEditor Enter the values ofthe independent variable in CI andthe values of the dependent variable 1 c2 The next tune you wish to enter data you ean press then 5 DataMatrix Editor andthen 1 rent Then simply elear the oldhsts and put in new ones 2 Make a scatter plnt orymrr dzt erlle stlll m the Data Edrtor press Defl ne Plat Setup nglrllglrtPlot landpress Make sure the Pl at Type ls setto Scatter If not use to lrrglrlrglrt the plot type and press 0 Use to hlghllght 1 Scatter and press ForMarmse Box You ear ehan changed Pl at Type lfyou wlsh E 39ene ceteeeneea Nu E ge ltjust as you Use to move the eursorto the box labeled x Type m cl and press Q to move the eursorto the boxlabeledy Type m c2 andpress MakesureUSe Freq and Categorleshs settoNo Press to return to the Data Edltor Press El GRAPH and then Zoom Choose meow y r yrsvyrivyn T If the data look llke a llne would be a good t nd the regresslon llrre Find the enrrelatinn ene ieiem and the regression lme Press El HOME to retum to the mam sereerl Pr tlrerramataMatrlx Edlto 1 Current Pres Calctogettlre calculatesereen ess r and then Use Freq and eteeeereea Nu Portal cul atl on Type presso anolehoose 5 Ll n Rea stare RegEu t runes 1n the x box enter cl andln the y box enter c2 yfeim and Memes Nu Moye down to Store Reg E0 to and press O and then seleet yl x and press Press agaln to see the regressron llne The equatron ofthe yl r y n yr y a ya myquot Press to elearthrs sereen r b c gee a r r 2 2 EW 3mg 3 3 R some t t 5 5 s 7 Esteem n p e u 4 new a y a WWW T Press El GRAPH n 5 Return your taleulatnr hack to normal graph made 39r t tyms g mslnmttumtl anolthen pres 00m andehooseoptlonasmomstd 5 Predict same values using the regresslnn line your data do not extrapolate Press El t ereen rnput value you wantto use and press V Solving EquationsFinding Zeros of Functions then pres and then 1 s L v e Type ln the equauon you wlsh to solve followed by the vanable you wrshto solye x e2x15x Don39tforgetto elose for for example 50 1 ve the parentheses Press VI Finding Points of Intersection of Curves If you want to nd where the graphs of x and gr rneet solve the equtron x gr as above Thls wlll glve you the r eoordnate of the pornt where they rneet Don39tforget to nd they eoordnate V11 Finding Maxima and Minima h u m deereasrng or vree versa Thls ls alsouseful m ndlng the range ofafuncuon press EH El GR The ealeulator m V quotquot V quot V quot39V Vquot T a lower bound to where the rnaxrrnurnrnrnrrnurn ls Use to rnove to the le ofwhere the rnaxrrnurnrnrnrrnurn ls Press Lower uuunna mu myqu y n yrsvyrivyn T l upper bound to where the rnaxrrnurnrnrnrrnurn ls Use to rnove to the nght ofwhere the rnaxrrnurnrnrnrrnurn ls Press andthe ealeulator wlll loeate the rnaxrrnurnrnrnrrnurn Eu gl both ofthese rnstead ofuslng to getto the le and nght ofthe rnaxrrnurnrnrnrrnurn you ean save trrne by slmp y typrng m anurnber For example when you are asked for alower bound m the above example1ust press the m and 1 keys and then srnee e 1 ls to the le of the rnaxrrnurnrnrnrrnurn we are lookung for Occaslonally you may get an answer sueh as el 4999999 5 You ean be reasonably eertarn the answerls e1 5 Also keep tn mmd that a ealeulator answer of 2 3333333 ls really 2 or If m nt make Knot the enaet answeruslng algebra l thatyou see all of the rnaxlrnarnlnlrna You vvlll needto nd them all