Plotting a piecewise-defined function | HP 39g+ Graphing guide

3	Function aplet
	About the Function aplet	3-1
	Getting started with the Function aplet	3-1
	Function aplet interactive analysis	3-9
	Plotting a piecewise-defined function	3-12
4	Parametric aplet
	About the Parametric aplet	4-1
	Getting started with the Parametric aplet	4-1
5	Polar aplet
	Getting started with the Polar aplet	5-1
6	Sequence aplet
	About the Sequence aplet	6-1
	Getting started with the Sequence aplet	6-1
7	Solve aplet
	About the Solve aplet	7-1
	Getting started with the Solve aplet	7-2
	Use an initial guess	7-5
	Interpreting results	7-6
	Plotting to find guesses	7-7
	Using variables in equations	7-10
8	Statistics aplet
	About the Statistics aplet	8-1
	Getting started with the Statistics aplet	8-1
	Entering and editing statistical data	8-6
	Defining a regression model	8-12
	Computed statistics	8-13
	Plotting	8-15
	Plot types	8-16
	Fitting a curve to 2VAR data	8-17
	Setting up the plot (Plot setup view)	8-18
	Trouble-shooting a plot	8-18
	Exploring the graph	8-19
	Calculating predicted values	8-20

ii

Contents

Image 4

HP 39g+ Graphing manual Plotting a piecewise-defined function, About the Solve aplet, Using variables in equations

Contents

User’s guide Edition Part Number F2224-90001 Printing History Edition December Contents Using variables in equations Plotting a piecewise-defined functionAbout the Solve aplet Getting started with the Polar aplet Confidence intervals One-Sample Z-Interval One-Proportion Z-Interval10-7 11-1 Variables and memory management 16-1 16-2Creating and editing programs 16-4 16-7 Glossary Resetting the hp 39g+ Service Regulatory informationOperating details Variables Home variables Preface Manual conventionsHewlett Packard’s Calculators web site can be found at Function, Polar, Parametric Preface On/off, cancel operations To cancelGetting started To turn on To adjust DisplayParts of the display Contrast Menu keys KeyboardInfrared or cable Aplet control keys Displays the Aplet Library menu. See Aplet library on Same Entry/Edit keysButton performs Shifted keystrokes Helpwith Math keys Commands MenusProgram Inactive keys Reset input form values Input forms Mode settings You use the Modes input form to set the modes for HomeCurrent aplet and Home give Same result Setting Options Number Function arguments. Comma modeLists and matrices, and to separate Uses periods dot as separators Aplets E-lessons Setting a modePress to return to Home Example x = cost and y = sint PolarSequence Sequence functions U in terms of n, or Another sequence, such as Un 1 Quad Explorer aplet Amplitude and frequency Keys Transforms Graph, with theseSeen by experimenting Aplet library Symbolic viewAplet views Select Plot-Table Plot view Numeric view Plot-Table view Plot-Detail viewSelect Plot-Detail Aplet view configuration Plot SetupOverlay Plot view Sketch view Views menu contains the Overlay Plot view Numeric Setup Symbolic Setup Where to startMathematical calculations Entering expressions Using Long results Negative numbers Scientific notation powers23 3 EEX Parentheses Explicit and implicit multiplicationEntering Calculates Sin 45 + π Input Output Last input Edit line Last output Getting started Storing a value in a variable Accessing the display history Clearing the display history Using fractionsSetting Fraction mode Setting fraction precision Select Fraction calculationsFraction Converting decimals to fractions Complex numbers Catalogs and editors About the Symbolic view Defining an expression Symbolic viewAplets and their views Aplet views Independent variable in the expressions is T U0. Define the nth term Aplets Evaluating expressionsSelect Function Home Setting up the plot Plot view setup About the Plot view ΘRNG Plot view settingsΘSTEP Reset plot settings Exploring the graph Trace a graph To move between relations To jump directly to a value To turn trace on/off Zoom within a graphZoom options Square SetFactors Auto Scale Un-zoom Now un-zoom To box zoom Box Zoom option lets you draw a box aroundOne diagonal of the zoom rectangle To turn on the menu-key Press to zoom in on the boxed area Other views for scaling and splitting the graph Views menu options Pixel=π/24 radian, 7.58, or Split the screenPress or About the numeric view Setting up the table Numeric view setup Numeric view settings NUM view menu keys Zoom within a table Exploring the table of numbersNumstart and Numstep Build a table Building your own table of numbersNumtype Build Your Own Build Your Own menu keys Clear data Reset the graph setup to the default settings Example plotting a circlePlot the circle, x 2+ y 2 = 9. First rearrange it to read Function aplet, specify the functions Display the functions in numeric form Function aplet About the Function apletGetting started with the Function aplet Open the Function aplet Define the expressions Set up the plot Plot the functionsSpecify a grid for the graph Plot the functions Change the scale Trace a graph Select AutoScale Times Analyse graph with FCN functions Select Root Select Slope Select Signed area To find the extremum of the quadratic Select Extremum Explore the table Display the numeric viewDisplay the table of values Symbolic definition A column Display the symbolic definition for the F1 columnSymbolic definition F1 is displayed at Bottom of the screen To display Select Plot FCN Function aplet interactive analysisOr to choose a variable FCN functions RootExtremum Slope Symbolic view. Displays Shading areaIntersection Cursor. You need to have at Plotting a piecewise-defined function Parametric aplet About the Parametric apletGetting started with the Parametric aplet Define the expressions Set up the plot Plot the expression Set angle measureSet the angle measure to degrees Select Degrees Plot a triangle graph over the existing circle graph Overlay plot Display the numbers120 Page Polar aplet Getting started with the Polar apletOpen the Polar aplet Select Polar Explore the graph Display the numbers Display the Plot view menu key labels Sequence aplet starts in the Symbolic view Sequence apletAbout the Sequence aplet Getting started with the Sequence aplet Plot Setup, set the Seqplot option to Cobweb Menu keys to assist in the entry of equations Select Cobweb Display the . Display the table of values for this examplePage Solve aplet About the Solve aplet Getting started with the Solve aplet Open the Solve apletDefine the equation Enter known variables Select Solve Solve the unknown variable Plot the equation Select Auto Scale Use an initial guess Interpreting results Plotting to find guesses Consider the equation of motion for an accelerating body To highlight T Plot the graph Press until the cursor is at the intersection Using variables in equations About the Statistics aplet Statistics apletGetting started with the Statistics aplet Select Statistics Enter dataTo move to the next column Select a fit in the Symbolic setup view Choose fit and data columns Explore statisticsSelect Linear Value is Setup plot Plot the graph Draw the regression curve Display the equation for best linear fitTo move to the FIT1 field Slope m is 425.875. The y-intercept b is Predict values To highlight Entering and editing statistical data Statistics aplet’s Numeric view keys are Statistics Copies the column variable or Variable expression to the edit line Data sets will need to be selected Clear is usedAgain before re-use Save data Plot a histogram of the data Edit a data set Delete data Insert data Sort data values Angle Setting Defining a regression modelTo choose the fit Fit models Computed statistics To define your own fit 7,8,15,16,17 Two-variableΣX2 To plot statistical data PlottingColumns for a linear fit only Plot types Histogram Box and Whisker Plot Scatter Plot Fitting a curve to 2VAR data Relative ErrorCorrelation coefficient Trouble-shooting a plot Setting up the plot Plot setup viewHistogram range Plotting mark 2VAR Connected points 2VAR Statistics aplet’s Plot view keys Erases the plot Calculating predicted values Find predicted values Statistics aplet Page Inference aplet About the Inference apletGetting started with the Inference aplet Open the Inference aplet Table below summarizes the options available Symbolic view Inference aplet’s Symb view keys Setup-NUM Select the inferential method Enter dataSelect Hypoth Test Test 1 ∝ Are explained in the feature of this aplet Importing sample statistics from the Statistics aplet If the Decimal Mark setting in the Modes input form Statistics aplet opens in the Numeric viewC1 column, enter the random numbers Produced by the calculator 529 295 952 259 925 592 Set up the interval calculation Open Inference apletInference Select Conf Interval Specify a 90% Confidence interval in the C field Display Numeric view Display Plot viewTo move to the C field Hypothesis tests One-Sample Z-TestMenu name Inputs Two-Sample Z-Test Results One-Proportion Z-Test Population 2 standardTest 1π Measures the strength of the evidence for a selected Two-Proportion Z-Test One-Sample T-Test Sample standard deviation With the α level that you Two-Sample T-Test Pooled? Confidence intervals One-Sample Z-Interval Two-Sample Z-Interval One-Proportion Z-Interval Two-Proportion Z-Interval One-Sample T-Interval Two-Sample T-Interval Pooled Critical T Critical value for T Using the Finance Solver Background 3 4 Compounding period -- which is Performing TVM calculations Example 1 Loan calculations Soft menu key. The resulting value is PV = $15,705.85 Example 2 Mortgage with balloon payment Calculating Amortizations To calculate amortizationsExample 3 Amortization for home mortgage To continue amortizing the loan Example 4 Amortization for home mortgage Using mathematical functions Math functionsMath menu Name. Note You do not need to press first Math functions by category Function categoriesSyntax Functions common to keyboard and menus Keyboard functions Value1+ value2 , etcEvalue E5 returns Returns LOG100 returns ABS1,2 returns Calculus functions Nthroot 8 returns∂ s1s1 2+3*s1 returns 2*s1+3 S1,2*X+3,X Complex number functions TaylorARG Conj Constants Hyperbolic trigonometry List functions Loop functions Matrix functions Polynomial functionsPolycoef POLYCOEF2,-3,4,-5 returns1,2,-25 Polyform PolyevalPolyroot Probability functions CombPerm Random Real-number functions Fnroot FracHMS→ →HMS MAX MINMOD Change Two-variable statistics RoundSign Truncate Symbolic functions IsolateLINEAR? Quad Test functions Quote Trigonometry functions Symbolic calculations Using formal variablesSEC SECvalue Finding derivatives Symbolic calculations in the Function apletTo find derivatives in Home To find derivatives in the Function aplet’s Symbolic view Show the resultSelect F2X and evaluate it You could also just define For example, to find the indefinite integral To find the indefinite integral using formal variablesThus, substituting X for S1, it can be seen that 11-24 Variables and memory management Introduction Storing and recalling variables To use variables CalculationsYou can use variables in calculations. The calculator Substitutes the variable’s value in the calculation Vars menu Open the Vars menuPress Move the highlight to the variables column Add the contents of two list variables, and to store Names or values of variables into programsExample Result in another list variable 12-6 That you can configure using Real part, and i representsVariable on page 15-5 for more Information on storing graphic object via To access an aplet X0, Y0 to X9, Y9 Symbolic view. SeeVariable Aplet variables on page R-7 Memory Manager Line, press and pressPage Matrices VectorsMatrices Matrix Variables Matrix Catalog keys Creating and storing matricesPOLYROOT1,0,-1,0XM1 To create a matrix in the Matrix Catalog To transmit a matrix Working with matricesOr column you are prompted to Make a choice Key Meaning Moves to the first row, last row, first If M2 is 3,4,5,6, then M21,2 returns To store one element Matrix arithmeticCreate the second matrix Matrices 13-7 To negate each Solving systems of linear equationsElement About functions Matrix functions and commandsSelect Real matrix Argument conventions ColnormCond Cross DET DOTEigenval Eigenvv Rank RownormRref Schur Examples SVDSVL Trace Reduced-Row Echelon Form Following set of equations x 2y + 3z = 14 2x + y z = Lists You can create, edit, delete, send, and receive named List catalog keys Create a list List edit keys Displaying and editing lists To display a listTo display one To edit a list A list To insert an element 1. Open the List catalogPress , and press 148 L12 List functions Deleting listsTransmitting lists To delete a list 2,3 returns 5,10,15 CONCATlist1,list2CONCAT1,2,3,4 returns 1,2,3,4 ∆LISTlist1 ΠLISTlist ΠLIST2,3,4 returnsPOSlist, element POS 3, 7, 12, 19,12 returns Finding statistical values for list elements ΣLIST2,3,4 returnsSorts elements in ascending order. SORTlist List, L1 Create L1 with values 88, 90, 89, 65, 70, Are now in column 1 C1 Aplet note view To write a note in Note viewYour work is automatically saved. Press any view key Or to exit the Notes view Contents of variables CommandsSpace key for text entry Alpha-lock for letter entry Sketch keys Aplet sketch viewTo draw a line To draw a box Draw keys Press to continue drawing, or press Mynote Opens the selected note for Begins a new note, and asksFor a name Another hp 39g+ or PC Press instead Contents of a Program Structured Programming Programming Program catalog Open Program CatalogBe simple-or it can be divided further into other Programs that perform smaller tasks Program catalog keys Create a new program Creating and editing programsPress Progrm to open the Program catalog Press to paste the command into the program editor On the left, use or to highlight a commandEdit a program 1. Press Progrm to Editing keys Using programs Run a program Debug a program Stop a program Transmit a program Customizing an aplet Aplet naming convention Example Configuring the Setviews menu option programs Save the aplet Setviews ’’’’ ’’’’18 ’’My Entry1’’’’EXP.ME1’’1’’My Entry2’’’’EXP.ME2’’3 ’’ ’’’’EXP.SV’’0 ’’’’’’EXP.ANG’’0 Programming commands’’START’’’’EXP.S’’7 Aplet commands CheckSelect Setviews Associating programs with your aplet Auto-run programs ViewNumber ProgramNameIncluding standard menu options Branch commands IF...THEN...ENDUncheck n 1XA Iferr trap-clause Then error-clause END IF... THEN... ElseEND CASE...END Iferr Then END Drawing commands RUNStop ARC Graphic commands →DISPLAY →GROBGrobnot Grobor Loop commands Do a + 1 X a Until a == Matrix commands Delcol DelrowEditmat Randmat Print commands Prompt commands Choose DispDisptime Disp 3A is 2+2 Input nametitle,labelhelpdefault GetkeyInput Editmat matrixname Stat-One and Stat-Two commands MsgboxPrompt Wait Stat-One commands Stat-Two commands Storing and retrieving variables in programs Plot-view variablesArea Axes Coord ExtremumFastRes Grid Hwidth IndepInvCross Isect Nmin / Nmax RecenterRoot S1mark-S5mark Simult SlopeStatPlot Umin/Umax Tmin / Tmax TracingTstep Xcross Xtick YtickXmin / Xmax Ymin / Ymax Symbolic-view variables R1...R9, R0 U1...U9, U0E1...E9, E0 S1fit...S5fit Numeric-view variables C1...C9, C0Digits Format NumCol NumFontNumIndep NumRow NumStep NumTypeNumZoom StatMode Sketch variables PageNumGraphicname X PageNum Extending aplets Creating new aplets based on existing aplets Solve Open the Solve aplet and save it under the new nameDegrees Using a customized aplet Resetting an apletChoose the sine formula in E1 Sending and receiving aplets Downloading e-lessons from the webHewlett-Packard’s Calculators web site can be found at Sorting items in the aplet library menu list To transmit an aplet To sort the aplet list To delete an aplet Reference information GlossaryExpression line# Cross matrix1,matrix2 Editor and catalog Matrix Two-dimensional array of values Record using the Program editorVector One-dimensional array of values Set to Comma and enclosed Resetting the hp 39g+ To erase all memory and reset defaultsTo reset using the keyboard Split screens If the calculator does not turn on Operating detailsBatteries To install the main batteries To install the backup battery Variables Home variables Area Root Extremum Slope Isect Function aplet variablesAngle Parametric aplet variables Parametric aplet variables are Category Available name Plot Polar aplet variables Polar aplet variables are Category Available names Plot Sequence aplet variables Sequence aplet variables are Category Available name Plot Solve aplet variables are Category Available name Plot Solve aplet variablesDigits NumCol Format NumRow Statistics aplet variables Math menu categories Math functionsMath functions are Category Available name Calculus Hyperb Category Available name Matrix Polynom Program constants Program commands Program commands are Category Command ApletBranch Print Status messages Function value, root, extremum Or intersection is not visibleCurrent screen Such as 0/0 Limiting Warranty Hp 39g+ Graphing Calculator Warranty period 12 months Limiting Warranty Service Canada 905 206-4663 or Rotc = Rest of the country Regulatory information USA Limiting Warranty Index Maximum real number 11-8 minimum real number Freeze 16-20 Line 16-20 Pixoff 16-20 Pixon 16-20 Tline Grobor Grobxor Inverse hyperbolic cosine 11-8 inverse hyperbolic functions Break Angle measure 1-10 decimal mark 1-11 number format Order of precedence 1-21 overlaying plots 2-16,4-3 11-8 Sending and receiving 16-8 structured Menu lists 1-8 speed searches Navigate around 3-8 numeric values 3-7 numeric view setup Index