Function app

The Function app enables you to explore up to 10 real- valued, rectangular functions of y in terms of x; for example, y = 1 – x and y = (x – 1)2 – 3 .

Once you have defined a function you can:

•create graphs to find roots, intercepts, slope, signed area, and extrema, and

•create tables that show how functions are evaluated at particular values.

This chapter demonstrates the basic functionality of the Function app by stepping you through an example. More- complex functionality is described in chapter 5, “An introduction to HP apps”, beginning on page 69.

Getting started with the Function app

The Function app uses the customary app views: Symbolic, Plot and Numeric described in chapter 5.

For a description of the menu buttons available in this app, see:

•“Symbolic view: Summary of menu buttons” on page 86

•“Plot view: Summary of menu buttons” on page 96, and

•“Numeric view: Summary of menu buttons” on page 104.

Throughout this chapter, we will explore the linear function y = 1 – x and the quadratic function y = (x – 1)2 – 3 .

Function app

111

Page 115

Image 115

HP Prime Graphing NW280AAABA manual Getting started with the Function app

Contents

User Guide HP Prime Graphing Calculator Product Regulatory & Environment Information Edition1 Part Number NW280-2001 Legal Notices Edition Printing HistoryJuly Page Contents Plot view Application Library App views Symbolic viewCommon operations in Plot view Zoom Trace Function app Computed statistics 233 Getting started with the Polar app 277 Getting started with the Parametric app 271 Variables Lists Status messages Basic integer arithmetic Manual conventions Preface Function, Polar, Parametric, Ans, etc Before starting Getting started On/off, cancel operations Display Sections of the display You are working in CAS view, not Be entered in uppercase when aUppercase when a key is pressed Lowercase when a key is pressed Navigation Touch gestures Keyboard Context-sensitive menu Primary entry and edit keys are Entry and edit keys Characters Minute, or second symbol accordComparison operators and Bool Ean operators Shift keys Adding text Math template Math keys Math shortcuts Original decimal representation Fractions Hexagesimal numbers236…. Press conce to see 219602 and again to see Pressing ca third time will cycle back to Return home H Enter 4BQ13 s6B23n 3BQ5 EEX key powers To select from a menu Menus Toolbox menus Input formsAlternatively, select the field and tap Home settings System-wide settings Becomes 1.23E9 in Engineer Becomes 123.46Fixed 2 format 23E2 in Scientific Or a+b*i Or in common mathematical Commands on the Math and CASShorthand. The default is to provide Menus are presented descriptively MM/DD/YYYY YYYY/MM/DD, DD/MM/YYYY, or Press SH Settings to open Specifying a Home setting Choosing an entry type Where to startAlways one-dimensional Mathematical calculations Textbook Examples that follow assume that the entry mode isEntering expressions RPN Reverse Polish Notation. Not available in CAS view R23jw14S j8nQ3 h45E Example Parentheses Sj85s9 Negative numbersAlgebraic precedence E45+Sz Explicit and implied multiplication Large results Reusing previous expressions and results To reuse the last Using the clipboardResult Sj2E Storing a value in a variableSjS+E Szj AQAcE Szj AaEExample To assign π2 to to the variable a Sharing data Complex numbersR2o3 Ay6E HP Prime to another When is tapped Online Help RPN Reverse Polish Notation Reverse Polish Notation RPNRPN is available in Home view, but not in CAS view History in RPN mode SzX3 Re-usingSample calculations Results Reverse Polish Notation RPN Swap Manipulating the stackStack Show an item Delete an item Delete all items CAS view Computer algebra system CAS Menu buttons in CAS view are Assigns an object to a variable CAS calculations 5Asjw6 Settings2Asj+3 Asw2 Standard or Scientific or Engineering Ments Radians or Degrees Recursive Replacement Tion above See also Recursive Evalua Computer algebra system CAS Computer algebra system CAS Exam Mode Press O+ A+ c Modifying the default configurationPress SH. The Home Settings screen appears Tap Don’t want disabled are not selected Before, the only base configuration will be Default Exam Creating a new configuration Activating Exam Mode Tap If a configuration other than Default To activate exam mode Cancelling exam mode Modifying configurationsTo change a configuration Deleting configurations To return to the default configurationTap Exam Mode screen appears Exam Mode An introduction to HP apps Equations Linear SolverSolve Explore equations in one or more real Application Library To delete an app Other options Test Symbolic viewApp views Confidence level, and select a type Symbolic Setup view Plot view Symbolic viewSolve Plot Setup view Numeric view Test selected in Symbolic viewAdvanced View a table of numbers generated by Graphing Symbolic view, and set the zoom factor Numeric Setup viewAdvanced Specify the numbers to be calculated Graphing N2f Quick exampleOpen the app 4Szf n2f jE Press SP Set the second θRNG field to 4π by entering Press PPress Pto return to Plot view and see the complete plot Θ column to be 1. You set this up in the Numeric Setup view Common operations in Symbolic viewNumeric View Modify a definition Add a definitionDefinitional building blocks From Home variables X2+X+ 2 *X2 Evaluate a dependent definitionSelect or deselect a definition to explore F9X=X2+Statistics2Var.PredY6 Delete a definition Choose a color for plots Symbolic view Summary of menu buttons Press SYto open Symbolic Setup view Common operations in Symbolic Setup viewOverride system-wide settings Restore default settings Zoom Common operations in Plot viewZoom factors Zoom options Shortcut press w By the X Zoom and Y Zoom settingsZoom setting Center on Apps, autoscaling rescales both axes Given the supplied x axis settings. ForGraph with the original plot settings Shows a representative piece of the plot Viewing Testing aZoom with Split-screen Out Shown, tap Integer SquareAutoscale Decimal Trig Trace To evaluate a definition To turn tracing on or off Configure Plot view Common operations in Plot Setup viewPlot view Summary of menu buttons Stats 1 Var only Parametric OnlyPolar only Sequence Only Sets the initial range of the y-axis. Note Sets the initial range of the x-axis. NoteThat here are two fields one for Panning and zooming Graphing methods Common operations in Numeric view Restore default settings Zoom options Zoom keys Zoom menu Evaluating Deleting data Custom tables Start typing a new value Only visible if Numtype is set to Numeric view Summary of menu buttonsSelect Ascending or Descending , Modifying Numeric Setup Common operations in Numeric Setup view Adding a note to an app Combining Plot and Numeric Views Creating an app Fibonacci in this example Asjw5 App functions and variables Select Statistics 1Var results MeanX Tap This opens a menu of app variables Getting started with the Function app Function app Function Open the Function app Define the expressionsRdw1 jw3E Open the Function app ISelect Set up the plot Plot the functions Trace a graph Change the scale Display the Numeric Setup view SMSetup Display Numeric view Set up Numeric view Substituted the values in the X column for x Press SJClear to reset all the settings to their defaultsExplore Numeric view To navigate around a table To go directly to a value To access the zoomOptions =or\ Analyzing functionsDisplay the Plot view menu To find a root of the quadratic function Intersection To find anIntersection of two Functions To find the slope of the quadratic function To find the signed area between the two functions Quadratic Function VariablesTo find Extremum Function Select Results and then the variable of interest Tap and select Named Extremum Summary of FCN operationsSlope Advanced Graphing app Getting started with the Advanced Graphing app ISelect Advanced Graphing Open the app Define the open sentenceJn2 + n5 128 Advanced Graphing app Advanced Graphing app 129 Edge You can move in any direction withinRegion. Use this option for Inequalities, for example Numeric view Display the Numeric view Explore Numeric view Trace in Numeric view Numeric Setup Sj3n2 Trace EdgeTrace PoI Exploring a plot from the Plot Gallery Plot Gallery Getting started with the Geometry app Geometry Plot Function 3seASsEWith plotfunc on the entry line, enter 3*sinx More Tangent Derivative point Create a AbscissaGB,slopeGC Add some calculations 140 Derivative changes by looking at a plot of it rather than Plot view in detailDerivative Point D is the point whose ordinate value matches 142 Moving objects Selecting anObject Hiding names Undoing Coloring objectsFilling objects Removing fill Moving about Clearing anClearing all Objects Plot view buttons and keys Key Result in Plot view Symbolic view in detail Tap either To move it down the list or Move it up Re-orderingEntries Hiding an object Tap Or press C To delete all objects, press SJ Can delete an object in Symbolic viewNumeric view in detail Deleting an Enter radiusGC Listing all 152 Points Geometric objects More Element 0 . . Notice Line Ngon Polygon Special Curve Thus enclosing the triangle Circumcircle is the circleThat passes through each Triangle’s three vertices Special Locus places Geometric transformations Given scale factor around a given point as center Tap Select ReflectionAxis and press E. The object is reflected across Symmetry axis defined in step GK,angleGK,GL,GM Select Transform Rotation 164 Barycenter Geometry functions and commandsSymbolic view Cmds menu Point Inter CenterDivisionpoint Element Point IsobarycenterMidpoint Orthocenter DrawSlp Point2dStop trace Erase trace Line BisectorExbisector Halfline Medianlinepoint1, point2, point3 MedianlineParallel Perpenbisector Draws a segment defined by its endpoints PerpendicularSegment Tangent Equilateral triangle0,6, v draws an equilateral EquilateraltriangleHexagon Equilateral triangle0,6 draws an equilateral IsoscelestriangleGA, GB, angleGC, GA, GB IsoscelestriangleIsopolygon Parallelogram Rhombus PolygonQuadrilateral Rectangle Square RighttriangleTriangle CircumcircleGA, GB, GC draws the circle CircleCircumcircle Conic Excirclepoint1, point2, point3 EllipseExcircle Hyperbola Parabola TransformIncircle Locus Draws the orthogonal projection of a point onto a curve InversionProjection Reflection RotateGA, angleGB, GC, GD,GK rotates RotationSimilarity Translation Measure Plot Measure Numeric view Cmds menu Area AffixAngle ArcLen Area4-x2/4, x=-4..4 returns 14.666… CoordinatesDistance Distance2 Parameq EquationExtractmeasure Ordinate Isconcyclic TestRadius Iscollinear Isorthogonal IselementIsequilateral Isisoceles Isrectangle IsparallelIsparallelogram Isperpendicular Harmonicconjugate Other Geometry functionsIssquare Convexhull Isrhombus IsharmonicIsharmoniccirclebundle Isharmoniclinebundle Polar LineHorzLineVert Openpolygon Reciprocation PowerpcPole Radicalaxis Verticesabca SingleinterVector Vertices 194 Getting started with the Spreadsheet app SpreadsheetTo open the Spreadsheet app, press Iand select Spreadsheet 196 Select cell C5 Select cell D1 Enter a formula to add up your takingsSelect cell C3 Enter a label for your total commission Select the heading cell for column C, tap and select Enter a label for your fixed costs Ancostse Navigation, selection and gestures Basic operations Cell naming Cell referencesMethod Enter Cost and tap Entering contentCOST*0.33 and tap Enter Statistics1Var.D1 Select Polynomial Find Roots External functions Format, both value and format, or both formula and format External referencesCopy and paste To copy one or more cells, select them and press SVCopy Referencing variables = Row2-√Row-1. The only Using the CAS in spreadsheet calculations Changes to Buttons and keysHandled by the CAS, but only Evaluates it Line is active Formatting options appear Formatting optionsFont Size Auto or from 10 to 22 point Format Parameters Spreadsheet functions Getting started with the Statistics 1Var app Statistics 1Var appStatistics 1Var Sample data in D1 Enters D directly to save you having to press two keys Symbolic view menu itemsMenu items you can tap on in Symbolic view are Editing. Tap when done 214 Entering and editing statistical data Configure a histogram plot for the data Setup Menu items you can tap on in Numeric view are Edit a data set1Var app open, return to Home view and enter Spreadsheet.A1A10 D7 E Delete data Insert data Generating data Sort data values Computed statistics Histogram PlottingPlot types To plot statistical data Bar graph Box-and-WhiskerNormal probability Line plot Data in descending Setting up the plot Plot Setup viewPareto chart Exploring the graph Menu items you can tap on in Plot view are Plot view menu items Dependent, y Statistics 2Var appGetting started with the Statistics 2Var app Advertising minutes Resulting sales $ Enter the advertising minutes data in column C1 2E1E3E5E5E4 Statistics 2Var Statistics 2Var app 225 Setup plot Plot the graph Display the equation Predict values Spreadsheet.A1A10 C7 E Buttons you can tap on in Numeric view are Numeric view menu itemsTap , make your change, and tap Descending Delete data Insert data Sort data values Fit types Defining a regression model Positive real value in L, or-if Where L is the saturation valueFits the data to a logistic curve For growth. You can store a COV SCOVΣXY SerrY Plotting statistical data Tracing a curve Tracing a scatterTracing order Connect Plot setupPlot view menu items Plotting mark Home view Predicting values Troubleshooting a plot Inference Inference appGetting started with the Inference app Open Test μ1 μ2, the T-Test on Symbolic view options Population standard deviation Alpha level for the test Select the inference method Enter dataTest 1 μ from the Type menu Sample mean Sample size Display the test results Plot the test results Open the Statistics 1Var app Clear unwanted data Enter data Importing statistics82.5 E 83.1 E 82.6 E 83.7 E 82.4 E 83 E Confidence Interval Calculate statistics Open the Inference appSelect inference method and type Import the data Tap on the Method field and select Numerically Hypothesis testsDisplay Results Menu name One-Sample Z-TestInputs Two-Sample Z-Test One-Proportion Z-Test Two-Proportion Z-Test This test measures the strength of the evidence for a One-Sample T-TestTest Z Test statistic Test Δ pˆ Difference between With the test Z-value Test μ1 μ2 Two-Sample T-TestEach sample from a different population, this test Sample 2 standard deviation Sample 1 standard deviationΑ level that you supplied One-Sample Z-Interval Confidence intervalsTwo-Sample Z-Interval Sample success count Sample size Confidence level One-Proportion Z-IntervalInt 1π Number of successes Proportions of successes in two populations Two-Proportion Z-IntervalMenu name Int π1 π2 Confidence interval for the difference between Two-Sample T-Interval One-Sample T-Interval Result Definition 258 Getting started with the Solve app Solve app AVjS.AU j+2AAAD One equationOpen the Solve app Clear the app and define the equation Solve the unknown variable Enter known variablesKph over a distance Is approximately 2.4692 m/s2 Matches the value of a you calculated above Where n is the number of the selected equationPlot the equation Select Auto Scale Select Both sides of En Open the Solve app Define the equations Enter a seed value Several equationsAXj+AYj S.16E AXwAYS. Q1E Solve the unknown variables Limitations Reversal Solution informationZero Sign No values satisfy the selected equation or expression Bad Guesses Constant?Value of the equation is the same at every point sampled Linear Solver Linear Solver appGetting started with the Linear Solver app Open the Linear Solver app. ISelect Coefficients and constants had been entered Define and solve the equations Solve a two-by- two system Menu items 270 Parametric Parametric appGetting started with the Parametric app Open the Parametric app 8ed? 8fd? Define the functions Degrees Set the angle measure Set up the plot Plot the functions 274 Tap .The table scrolls to the value you entered 276 Open the Polar app Open the Polar app ISelect Polar App opens in Symbolic viewPolar app Getting started with the Polar app 5Szf dn2 fdj Set angle measure Set up the plotDefine the expression 5πcosθ/2cosθ2 Plot the expression Explore the graph 280 Polar app Getting started with the Sequence app Sequence app Sequence App opens in Symbolic view Define the Fibonacci sequence+ E Open the Sequence app ISelect Select Stairstep from the Seq Plot menu Plot the sequence Display Numeric view Explore the table of values RQFand Set up the table of valuesDefine the expression Setup the plot Another example Explicitly-defined sequences Plot the sequence Explore the table of sequence values Getting Started with the Finance app Finance app 288 Cash flow diagrams Time value of money TVM PMT TVM calculations Another example 292 To calculate amortizations Calculating amortizations Amortization graph Finance app 295 Open the Triangle Solver app ISelect Triangle Solver appGetting started with the Triangle Solver app Tapping Specify the known values Solve for the unknown values Choosing triangle types Special cases Triangle Solver app 299 Linear Explorer app Explorer apps Between them by tapping or Graph mode Test mode Equation mode Tap to enter Explorer Quadratic Explorer appOpen the app Quadratic Graphs that are harder match by tapping Respectively Equation modeIts value. When you are ready, tap To see if you Tap To see the correct answer and tap Exit Test mode Trig Explorer Trig Explorer app Are available. Tap To switch toGraph by pressing Cursor keys. All four keys Now press the cursor keys to select each parameter Tap to see the correct answer and tap to exit Test mode All the functions and commands Functions and commands 308 Abbreviations used in this chapter Keyboard functionsNORMALICDFμ,σ,p ALOG3 returns +,w,s, nShex E5 returns Efg +2*i returns -1-2*i 1returns2returns Numbers Math menu Example XPON123456 returns 5 since 105.0915... equals ArithmeticMaximum Maximum. The greater of two values Modulus Modulo. The remainder of value1/value2 Example ARG3+3*i returns 45 degrees modePercentage x percent of y that is, x/100*y Example Trigonometry Probability Hyperbolic Normal Random real number with normal distribution Nμ,σ PERM5,2returns STUDENTn,x RANDSEEDvalueNORMALDμ,σ,x NORMALD0.5 and NORMALD0,1,0.5 both return Is a real number FISHERCDF5,5,2 returns CHISQUARECDFn,kCHISQUARECDF2,6.1 returns FISHERCDFn,d,x List Special Matrix Algebra CAS menu Denoma/b Syntax substExpr,Var=valuePartfracRatFrac or Opt Numera,b DiffExpr,var DiffExpr,var1$k1,var2$k2 CalculusLimitExpr,Var,Val,Dir1, 0 DivergenceExpr1, Expr2, …, ExprN, Var1, Var2, …, VarN SeriesExpr,Equalvar=limitpoint,Orde r,Dir1,0,-1SumExpr,Var,Real1, Real2,Step CurlExpr1, Expr2, …, ExprN, Var1, Var2, …, VarN IbpufVar, uVar, Var, Real1, Real2 GradExpr,LstVarHessian Returns the Hessian matrix of an expression HessianExpr,LstVar DivpcPoly1,Poly2,Integer PrevalExprFvar,Reala,Realb,VarSumriemannExprXpr,Lstvar1,var2 TaylorExpr,Var=Value,Order Solve CZerosExpr,Var CZerosExpr1, Expr2,…,Var1, Var2,… ZerosExpr,Var or zerosExpr1, Expr2,…,Var1, Var2,…Zerosx2-4 returns -2 CsolveEq,Var CsolveEq1, Eq2,…, Var Rewrite Exp2trigExpr TexpandExprExp2powExpr Pow2expExpr Acos2atanExpr Asin2atanExprSin2costanExpr Acos2asinExpr Tan2sincosExpr Atan2asinExprAtan2asinatan2*x returns Atan2acosExpr TlinExprTrig TrigcosExprTrigtanExpr Atrig2lnExpr Integer PrevprimeInteger GcdIntgr1, Intgr2,…IsPrimeInteger NextprimeInteger Powmoda, n, p,Expr,Var PolynomialIquoIntgr1, Intgr2 IremIntgr1, Intgr2 GcdPoly1,Poly2 CoeffPoly, Var, IntegerDivisPoly or divisPoly1, Poly2,… FactorsPoly or factorsPoly1, Poly2,… Poly2symbVector, Var Symb2polyExpr,Var Symb2polyExpr, Var1, Var2,…PcoefVect QuoList1, List2, Var QuoPoly1, Poly2, Var PminMtrx,VarRemList1, List2, Var RemPoly1, Poly2, Var SturmabPoly,Var,a,b ContentPoly,VarDegreePoly FactorxnPoly HermiteInteger CyclotomicIntegerGbasisPoly1 Poly2…, Var1 Var2… GreducePoly1, Poly2 Poly3 …, Var1 Var2… Tchebyshev2Integer LagrangeX1 X2…, Y1 Y2…LaguerreInteger Tchebyshev1Integer Plot PlotodeExpr, Var1, Var2, X0, Y0 App menuPlotlistX1, Y1, X2, Y2, … Function app functions SOLVEX2-X-2,X,3returns2 Solve app functionsSpreadsheet app functions SOLVEEn,var,guess As in SUMB7C23 FunctionNameinput,optional Parameters=STAT1A25A37 =STAT1A25A37,h n Finance app Calculates the arithmetic mean of a range of numbersFor example, AVERAGEB7B23 returns the arithmetic Specify a block of cells, as in AVERAGB7C23 Place column headers Place row headers Serr Second column is treated as the weight of the firstColumns are multiplied to generate a data point Set to STAT1A25A37 REGRSInput range,model, configurationSTAT1A25A37,h n x σ Example REGRSA25B37,2 PredXmode, y, parameters PredYPredX PredYmode, x, parameters HypZ1mean The one-sample Z-test for a mean HypZ1mean x, n,μ0,σ,α,mode, configurationHypZ1mean0.461368, 50, 0.5, 0.2887, 0.05 HypZ2mean0.461368, 0.522851, 50, 50, 0.2887, 0.2887, 0.05 HypZ1propHypZ1propx,n,π0,α,mode HypZ1prop21, 50, 0.5, 0.05,1 HypZ2prop HypZ2prop21, 26, 50, 50, 0.05 Mode Specifies which alternative hypothesis to use ≠ μ0HypT1mean x ,s,n,μ0, α,mode,configuration HypT1mean The one-sample t-test for a mean ConfZ1mean x ,n,s, C,configuration HypT2meanx1,x2,s1,s2, n1,n2, α,pooled,mode, configuration ConfZ2mean0.461368, 0.522851, 50, 50, 0.2887, 0.2887 ConfZ2mean x1, x2, n1, n2,s1,s2,C, configurationConfZ1propx,n,C,configuration ConfZ1mean0.461368, 50, 0.2887 ConfT1mean ConfZ2propConfZ1prop21, 50 ConfT2mean0.461368, 0.522851, 0.2776, 0.2943, 50, 50, 0 ConfT2mean x1, x2, s1,s2,n1, n2,C,pooled, configurationStatistics 1Var app functions ConfT1mean0.461368, 0.2776, 50 SetFreq Do1VStatsSetSample SetDepend Statistics 2Var app functionsResid Do2VStats HypZ1mean Inference app functionsSetIndep DoInference Critical value of π associated with the critical Z-value Test π valueHypZ2mean x1, x2, n1, n2,σ1,σ2,α,mode Critical value of the statistic associated with HypT1meanOrder Test Δπ value HypT2meanx1,x2,s1,s2, n1,n2, α,pooled,mode ConfZ2mean ConfZ1meanConfZ1prop Two proportions. Returns a list containing in order CalcFVNbPmt,IPYR,PV,PMTV,PPYR,CPYR,BEG Finance app functionsCalcFV Solves for the future value of an investment or loan CalcPV CalcIPYRCalcNbPmt CalcPMT Solve3x3 Linear Solver app functionsTriangle Solver app functions Solve2x2 SSAside,side,angle AASangle,angle,sideASAangle,side,angle SASside,angle,side DoSolve Linear Explorer functionsSolveForYIntercept DELTAa, b, c Quadratic Explorer functionsCommon app functions SOLVEa, b, c Enter Sequence.UNCHECK2 Ctlg menuFunction.CHECK1 UNCHECKDigit Change Percent change from x to y. Returns 100*y-x/x Percent of y. Returns x/100*y Example 3,4.*3,4,5,6 gives 3,8,15,24 List1.*List2 or Matrix1.*Matrix2List.Integer or Matrix.Integer Var=expression Abcuvx2+2*x+1,x2-1,x+1 returns 1/2 -1/2 A2qMatrix, Var1, Var2…A2q1,2,4,4,x,y returns x2+6*x*y+4*y2 AbcuvPolyA, PolyB, PolyC, Var Append Appends an element to a list or vector CatObject1, Object2,… BasisMatrixCanonicalformQuadraticExpr,Var Canonicalform2*x2-12*x+1 gives 2*x-32-17 ColDim Returns the number of columns of a matrix Complexrootx3+8, 0.01 returns Companion Returns the companion matrix of a polynomial CorrelationList or correlationMatrix ContainsList, Element or containsVector, ElementContains0,1,2,3,2 returns CopyVarVar1,Var2 Returns Enters the mathematical constant e Euler’s number Eval Evaluates an expression Eigenvals Returns the sequence of eigenvalues of a matrix Even1251 returns EvalcExprEvalfExpr,Integer Evalf2/3 gives ExprX+10 returns 100, if the variable X has the value Expr Parses the string String into a number or expression FMinx2-2*x+1,x gives FMaxExpr,VarFMax-x2+2*x+1,x gives FMinExpr,Var GaussExpr,VectVar FsolveExpr,Var,Guess or Interval,MethodFunctiondiffFnc Functiondiffsin gives x→cosx HamdistInteger1, Integer2 GramschmidtVector, FunctionHalftanhyp2expExprTrig Halftanhyp2expsinx+sinhx returns HeavisideReal IcontentPoly,VarIcontent24x3+6x2-12x+18 gives Head1,2,3 gives Inv Returns the inverse of an expression or matrix Interval2center Returns the center of an interval IPart4.3 returns JacobisymbolInteger1, Integer2Jacobisymbol132,5 gives IPartReal or iPartList Lin Returns an expression with the exponentials linearized Logb Returns the logarithm of base b of a Lname Returns a list of the variables in an expression Mat2list Returns a list containing the elements of a matrix Lvar Returns a list of variables used in an expression Median1,2,3,5,10,4 gives MeanList1, List2 or meanMatrixMean1,2,3,1,2,3 gives 7/3 MedianList1, List2 or medianMatrix MultcconjugateExpr ModgcdPoly1,Poly2Modgcdx4-1,x-12 gives MRowExpr, Matrix, Integer NormalizeVector or normalizeComplex NDerivfx,x,h returns fx+h-fx-h*0.5/hNormalExpr Normal2*x*2 gives 4*x PIECEWISE⎪ PI Inserts π Plotpolarπ/2x, x=-π..π plots a partial spiral PlotparamfVar+i*gVar, Var= IntervalPlotparamcost+i*sint, t=0..2*π plots the unit circle PlotpolarExpr,Var=Interval POLYCOEF-1, 1 returns 1, 0 PoleCrcle,LinePolecircle0, 1, line1+i, 2 returns point1/2,1/2 POLYCOEFVector or POLYCOEFList POLYROOTPoly or POLYROOTVector PolygonscatterplotMatrixPolynomialregressionList1, List2, Integer Polynomialregression1, 2, 3, 4, 1, 4, 9, 16,3 returns 0 1 0 Prepend1,2,3 gives 3,1,2 PowerregressionList1, List2Powerregression1, 2, 3, 4, 1, 4, 9, 16 returns 2 Powerpccircle0,1+i,3+i gives Purge Unassigns a variable name Quote Returns an expression unevaluated ⎠ returns Remove6,1 2 6 7 returns 1 2 Reducedconicx2+2*x-2*y+1 returnsRefMatrix RemoveElement, Vector or removeElement, List Restart Purges all the variables Residue Returns the residue of an expression at a value Example Gives RowDim Returns the number of rows of a matrix Signature Returns the signature of a permutation Sqrt Returns the square root of an expression Sto Stores a real or string in a variable Transpose Returns a matrix transposed without conjugation Sylvester Returns the Sylvester matrix of two polynomials Type Returns the type of an expression e.g. list, string Returns the square of an expression When Used to introduce a conditional statement Inserts the imaginary number Creating your own functionsExpr Function field, enter the function. eAA+fABAC Variables AaE Working with Home variablesResult is written to history Multiply a by AAxotwAS. Sq1o2 o3 E Working with user variables Working with app variablesExample 3 You can also store objects in variables More about the Vars menu Qualifying variables Home variables Home variables are accessed by pressing aand Tapping AAngle ADigits AComplex AFormat App variablesFunction app variables NumStart NumType NumStep NumZoom NumIndep Results variables Geometry app variables ColWidth RowHeight Category Names Symbolic PlotSpreadsheet app variables Solve app variables NumXStart Advanced Graphing app variablesNumYStart NumType NumXStep NumXZoom NumYStep NumYZoom Statistics 1Var app variables MaxVal NbItemMinVal MedVal Statistics 2Var app variables ΣCov CorrCoefDet SCov SerrY Inference app variablesContains the sum of the dependent values Y Prob CritScoreCritVal1 CritVal2 NumStart NumType NumStep NumZoom Parametric app variables NumIndep NumType NumStart NumZoom NumStep Polar app variablesFinance app variables Θmin Recenter Quadratic Explorer app variables Linear Solver app variablesTriangle Solver app variables Linear Explorer app variables Sequence app variables Trig Explorer app variablesCategory Names Modes Length Acceleration Units and constantsUnits Unit categories Palette of prefixes Unit calculationsPrefixes Units menu includes an entry that is not a unit +5 SF MKSA8.175cm/s returns .08175m*s-1 Unit tools UFACTOR100C,1A returns 100A*s Physical constantsUSIMPLIFY5kg*m2/s2 returns 5J Value or measurement? Avogadro, NA List of constants 450 Create a list in the List Catalog Lists = or \ =or \ List EditorList Editor Buttons Keys To insert an element To edit a listA list To createa list Deleting listsLists in Home view To delete a list To display one To store a listAj7 To display a list 2,3 returns 5,10,15 List functionsTo send a list Data on page 44 for instructions Aajo Make ListSort Menu format Reverse Concatenate Position Size Aj5 E Aj5E Ad1E Finding statistical values for listsAj1E Aj1 Beginning on page 211, for the meaning of each statistic Vectors MatricesMatrices POLYROOT1,0,-1,0M1 Creating and storing matrices Editor Working with matricesMatrix Editor To create a matrix in the Matrix Editor View Matrices in HomeTo store a matrix To display a matrix Matrixnamerow,column Matrix arithmeticR1o2 To send a matrix Divide by a scalar E3 EHAQ1 + To multiply AQ1k5 AQ1sAAQ1kQ Q1 n AQ2 Solving systems of linear equations 2E3E Tap in cell R1, C3 E 1E1E Q1E4EQ1 Commands Matrix functions and commandsSns AQ1E TRN ⎜ Matrix functionsArgument conventions TRN matrix IDENMATsize Rref matrixRref 3,2,3,4 Cos1 -sin1sin1 cos1 JordanBlockExpr,n0 JordanBlock7,3 returns 0 7 1 0 0 Hilbertn Rownorm ⎜ Rank Specnorm ⎜Specrad ⎜ Cond Eigenvv EIGENVALmatrix37228… -0.37228… Eigenvv matrix IhermiteMtrxA CholeskymatrixExample CAS view Cholesky ⎜ Ismith ⎜ HessenbergMtrxA278 IsmithMtrxA LUmatrix LSQmatrix1, matrix2LSQ P*A=L*U SVD ⎝ QRmatrix A,var1,var2SCHURmatrix Example Schur ⎛⎜ 1 2 ⎞⎟ returns L2normVect 4649… 0.3659…Cross 1 2 , 3 4 returns DOT 1 2 , 3 4 returns MaxnormVect or Mtrx ExamplesMaxnorm 1 2 3 -4 returns + y z = 5 2x y = 2y + z = 488 Begins a new note, Features. See belowOpens the selected note for Editing Rename renames the selected note To create a note from the Notes CatalogOpen the Note Catalog To create a note for an app Are adding or editing a note Keys With lowercase locked, make next character uppercase Make the next character upper-case Text formatting Mathematical InsertingExpressions Sharing notes Pixon xposition, yposition ,color HP Prime Programs Command StructureProgramming in HP PPL Pixon xposition, yposition END Program CatalogProgram Structure Comments Export Myprogam Begin Program Catalog buttons and keys Open Program Catalog =or S\ Myprogram Creating a new program Program Editor Or S=and Checks the current program for errorsStrings Drawing Matrix App Functions Integer More Press Jto return to the main menu Begin and END For N from 1 to 3 do Tap Myprogram to expand the menu and select Myprogram Run a Program Parameters Debug a ProgramMulti-function Programs Program Catalog, select Edit a program Copy a program or part of a program 510 To share a program HP Prime programming languageVariables and visibility Export Radius Export Getradius Begin Inputradius END Programming in HP PPL 513 Return 1+RANDINTN-1 Program RolldieProgram Export Rolldien Return 1+RANDINTn-1 END L2roll+1 L2rollRolldie ROLLDIEn User Keyboard Customizing key presses User modeBegin Return 1+RANDINTN-1 END Re-assigning keys Internal name of keys and key states Key names KDiv KAMath App programs View text, function Using dedicated program functions Redefining the View menuResets or Initializes an app Starts an app Customizing an app DiceSimulation Tap Enter a name for the new app such as View Roll Dice,ROLLMANY Dicesimvars RolldieExport SIDES,ROLLS Export DiceSimulation Begin END Until Sides =4 STARTVIEW7,1 END SidesBegin Repeat SIDES= Floorsides If SIDES2 then Sides END STARTVIEW1,1 ENDSTARTVIEW0,1 END Export ROLLS,SIDES Export Dicesimvars Begin Roll Dice Program commands Export SQM1X Begin Return END Commands under the Tmplt menu BlockBegin END Syntax Begin command1 command2… commandN END Branch Loop Default commands ENDCase Export Drawpattern Begin Export Maxfactorsn BeginMSGBOXMax of + max + factors for +result MAXFACTORS100 END Wait RectExport ISPERFECTn INPUTSIDES,Die Sides,N = ,Enter num sides,2 +1 d END Return sum==n ENDExport Perfectnums Begin Export Sides Export Getsides Begin Repeat Syntax Export FunctionName VariableFunction Export Syntax Export var1, var2, …, varn Char Syntax CHARvector or CHARinteger Commands under the Cmds menu Strings INSTRINGvanilla,van returns Instring banana,na returns StringF1, when F1X Cosx = Cosx666666666667 String Drawing Ymax Pixels and Cartesian Grobhpg Getpix Syntax GETPIXG, x, yGETPIXPG, x, y Grobh Syntax Grobhg INVERTPG, x1, y1, x2, y2 GrobwpgPIXOFFPG, x, y PIXONPG, x, y ,color Pixon Syntax PIXONG, x, y ,color Wait END Export BOX Begin Rect RECTP40,90,#0 +sign*4/2*K-1 a Export Piseries BeginLocal sign K=2 A=4 sign=−1 Rect TEXTOUTPN=,0,0 Textoutppi APPROX=,0,30 Repeat Addrow Syntax ADDROWmatrixname, vector, rownumber Sign*-1 sign K+1 KUntil END Addcol Syntax ADDCOLmatrixname, vector, columnnumber SUB Syntax SUB name, start, end Replace Syntax REPLACEname, start, objectScale Syntax SCALEname, value, rownumber Scaleadd Syntax Scaleadd name, value, row1, row2 App Functions Bitand Syntax BITANDint1, int2, … intn Commands →R Syntax B→R#integerm Bitsl Syntax BITSLint1 ,int2Getbase Syntax GETBASE#integerm Choose Syntax CHOOSEvar, title, item1, item2,…,itemn Getbits Syntax GETBITS#integerExample GETBITS#22122 returns #20h or →B Syntax R→Binteger Setbits Syntax SETBITS#integerm ,bits Taps Example EDITMATM1 edits matrix M1 Getkey Syntax Getkey Editmat Syntax EDITMATmatrixvar Export Sides Export Getsides Input Syntax INPUTvar ,title, label, help, resetBegin INPUTSIDES,D ie Sides,N = ,Enter num sides,2 END Export Areacalc Begin Msgbox Syntax MSGBOXexpression or string ,okcancel? Programming in HP PPL 553 Execon Syntax EXECON&expr, List1, list2,… Executes the function or returns the variable usingMore CAS Syntax CAS.function or CAS.variable Example ITERATEX2, X, 2, 3 returns Example →HMS54.8763 returns 5452′34.68″EXECON&23+&1,1,5,16,4,5,6,7 returns 7,12 Variables and Programs Programming in HP PPL 557 Cursor App variablesPlot view variables Axes Labels GridLinesHmin/Hmax Hwidth Θmin/θmax Nmin/NmaxRecenter S1mark-S5mark SeqPlot Tstep Θstep Polar Tmin/TmaxXtick Ytick Xmin/Xmax Yzoom Symbolic view variablesYmin/Ymax Xzoom H1...H5 F0...F9H1Type...H5Type S1...S5 R0...R9S1Type...S5Type X0, Y0...X9,Y9 TypeU0...U9 NumIndep Numeric view variablesC0...C9 D0...D9  NumType-forAutomatic default  NumType-forBuildYourOwn  NumStep where n NumXStep where n  NumYStep where n Alpha Conf  NumXZoom where n NumYZoom where n Inference app variables  Mean2 Mean1Mean2  Mean1 Difference of two means or two proportions, sets  Pooled-for not pooled defaultPooled  Pooled-for pooled Variables Finance appCPYR PMTV NbPmtIPYR NbPmt Triangle Linear Solver app variablesSolver app AngleC SideCAngleA AngleB Home Settings Language HComplexDate Time Signed EntryBase Bits AComplex SymbolicSetup AAngle  AFormat AFormat 580 Basic integer arithmetic Default base Binary, Octal, Decimal or Hex Changing the default base Mixed-base arithmetic Examples of integer arithmetic Integer manipulation These are described in Integer, beginning on Base functions Glossary Catalog Symbolic, and Symbolic Setup Matrix Two-dimensional array of real orRecord using the Program Editor Vector One-dimensional array of real or 590 If the calculator does not turn on TroubleshootingTo reset Calculator not responding Status messages Operating limits Apps, matrices, lists, notes, or Correct. Look up the functionName in the index to find its Proper syntax 594 Cables Product regulatory informationFederal Communications Commission notice Modifications 596 European Union Regulatory Notice 598 Substances ChemicalParliament and the Council. a chemical information 600 Index CAS 54 Menu 324-347 settings 30, 55 view370-371 Functions 118-122, 348 variables 366-369 299-301 606 Samples 514-516, 524-527 structure Zoom 88-94 points Polar app 70, 277-280 variables 215 Solve app 70, 259-266 functions 349 limitations 264 messages App 109, 558-579 CAS Types of 89-90