Graphing Instructions Teacher Notes

Graphing a Function Instructions (TI-Nspire)--Teacher’s EditionI. Enter Function1. New Graphs & Geometry page – c22. Enter the function in the Entry Line (this may be other than f1(x) if other functions exist in the currentproblem).3. Press ·.** The Entry Line is automatically hidden. Press e to view Entry Line and d to hide it.Teachers’ note: you can also toggle between showing the Entry Line and hiding it by pressing / GII. Change WindowTeachers’ note: “method 2” changes the window the way we are accustomed to on the TI83/84/89. It may be themost comfortable place to start.Method 1: Grab & drag plane and/or tick marks on the axes.Method 2: Enter specific window settings - b41.Method 3: Use Zoom functionality - b4, then select zoom option.1

III. View Table1. New Lists & Spreadsheet page – c3 2. Create Function Table –/T ( or b5)3. Select your function, then press ·. 4. Modify table settings – b53.Teachers’ Note: Notice there’s still a choice of “auto” or “ask” for the dependent variable. Play with it ifyou want…. but it doesn’t do what students typically hope for. Keep in mind that a calculator page will belinked to the same f1(x) entered in graphs & geometry, and we can do operations on that calculator screenas shown on the screen shot below.2

IV. Transforming GraphsCertain functions can be manipulated directly on the graph itself, and their corresponding equation changeswith this manipulation.For example, try graphing the function2f 1( x) x 4x 3 .Perform a stretch. Position the cursor on a side of the parabola until the õ symbol appears (seefigure 1, below), and press /xto grab the graph (or just hold x). Use the NavPad keys tostretch and/or flip the graph and press d when complete. The equation for the graph isautomatically updated in f1(x).Perform a translation. Position the cursor near the vertex of the graph until the ö symbol appears,and press /x, to grab the graph. Manipulate with the NavPad keys just like above. Onceagain, the equation itself is changed (Figure 2).Figure 1 Figure 2Here are some common forms of functions which can be manipulated: Linear function of the form f 1( x) b, where b is a constant Linear function of the form f 1( x) axbwhere a and b are constants.2 Quadratic function of the form f 1( x) ax bxcwhere a, b and c are constants.2 Quadratic function of the form f 1( x) a( xb)cwhere a, b and c are constants.axb Exponential function of the form f 1( x) e cwhere a, b and c are constants.ax Exponential function of the form f 1( x) be cwhere a, b and c are constants.axb Exponential function of the form f 1( x) de cwhere a, b, c and d are constants. Logarithmic function of the form f 1( x) aln( cxb)dwhere a, b, c, and d are constants. Sinusoidal function of the form f 1( x) asin( cxb) d where a, b, c and d are constants. Cosinusoidal function of the form f 1( x) acos( cxb) d where a, b, c and d are constants.3

V. Creating Sliders*These are very useful for demos. The process of creating a slider is slightly more user-friendly on thecomputer software (rather than creating it on your handheld).One of the most compelling features of the TI NSpire is the ability to use sliders to manipulate functions.This provides a dynamic tool for exploring many of the functions that we teach and can help studentsdiscover the relationships between the equations of functions and their graphs.1) Type in the standard form of a function, such aslike to use as the constants of the function.2f 1( x) ( x b)c , using whatever variable you’d2) Insert slider by going tob, 1: Actions, A: Insert Slider (figure 1). You can type any of yourslider variables (in this case b or c) directly over the “v1” (figure 2). Once you have named a slidervariable, the variable becomes bold print in the function notation.3) Change the slider settings by “right clicking” or using /b, choose 1: Settings, and tabthrough the options (figure 3) to set the slider range. Select OK to save.4) Repeat this process for as many slider variables as you have in your function.*Note: Each slider will initially be placed in the same location on your screen. You can move thesliders by holding x over any of them and sliding them to another location on your screen.Figure 1 Figure 2 Figure 35) To manipulate the sliders, you can either hold down the xdirectly on the slider, or click directlyonly the current value of the slider variable and type whatever value you would like to insert.Figure 4 Figure 54

VI. Graphing parametrically defined relationsIf you press b when on a Graphs & Geometry page, thesecond option allows you choose “Parametric” as a graphtype. (Notice this is also where you can change to a “Polar”or a “Sequence” graph type….)For the most part, parametric graphing on the NSpire-CASfunctions as it did on the TI83/84/89. Notice, however, thatthe settings for the parameter t are in the equation editor, notwith the other window settings.Because the processor on the TI-Nspire CAS is so fast, thegraphics display instantaneously and we no longer can“watch” the graph trace as it is created, no matter how smallwe set the tstep. However, we can use “Graph Trace” (b,5, 1) and watch the cursor move around the curve.Unlike the TI calculators we have used in the past, whentracing on a parametric curve, you can move directly fromtmax back to tmin. (The calculator doesn’t “get stuck” at thestart and end of the t-interval.)There has been some conversation on the Nspire Google group (http://groups.google.com/group/tinspire/)on the topic of showing the path traced. One quick “workaround” to show the path is to construct apoint on the curve and attach a slider to that point. You may be interested in playing with the TI-Nspiredocument “Parametric Friend,” created by a teacher in Indianapolis (Sean Bird). This TNS documentis saved on the G-drive.VII. Graphing polar functionsIf you press b when on a Graphs & Geometry page, the third option allows you choose “Polar” as agraph type. Just as with parametric curves, the range and step for the independent variable are set inthe equation editor.Again, due to fast processing speed, we no longer can see the path of a polar graph as it is traced. Justas with parametric curves, we can use “Graph Trace,” or construct a point on the curve and attach aslider. There is also a “Polar Friend” TNS document saved on the G-drive.5