TI-89 Calculator

Graphing a Function

  1. Press ◆ semicolon, then F1 to open the Y= editor.

  2. Input the function, with x as the variable.

    Calculator screen showing the function y1 = x³ + 5.X² - 7.x

  3. Press ◆ semicolon, then F2 to input window settings.

    Graphing calculator window settings with X range -10 to 10 and Y range -200 to 200.

  4. Press ◆ semicolon, then F3 to display the graph.

    This graph, likely from a TI-Nspire calculator, shows the plot of a piecewise-defined function

  5. To evaluate the function you input into the y1 equals field of the Y= editor at a given value of x, first press Home to display the home screen. Input Y1 left parenthesis, then the given value of x, and then a right parenthesis. Then press the Enter key.

    calculator screen, showing y1(5)

Graphing a Piecewise Defined Function with Two Pieces

  1. Press ◆ semicolon, then F1 to open the Y= editor.

    Calculator screen showing Plots.

  2. Press Catalog, then dot to select when left parethesis.

    Calculator catalog screen showing functions like when(, While, and xor).

  3. Press the Enter key. Using x as the variable, input the domain of the first function as an inequality, then a comma, input the first function, then a comma, input the second function, and then input a right parenthesis.

    Calculator screen with Y1 defined as a piecewise function using when(x<0, x², …)

  4. Press ◆ semicolon, then F3 to display the graph.

    Graph of piecewise function forming a V-shape on calculator screen

Graphing a Piecewise Defined Function with Three Pieces

  1. Press ◆ semicolon, then F1 to open the Y= editor.

    Blank function entry screen with Y1 selected on calculator.

  2. Press Catalog, then dot to select when left parethesis.

    Calculator catalog screen showing functions like when(, While, and xor).

  3. Press the Enter key. Using x as the variable, input the domain of the first function as an inequality, then a comma, input the first function, then another comma.

    Calculator screen with Y1 defined as a piecewise function using when(x<0, x², …)

  4. Press Catalog, then dot to select when left parethesis, and then press the Enter key.

  5. Input the domain of the second function as an inequality, then a comma, input the second function, then a comma, input the third function, and then input two right parentheses (one for each when left parenthesis function).

    Calculator screen showing a three-piece piecewise function defined in Y1.

  6. Press ◆ semicolon, then F3 to display the graph.

    Graph of a three-piece piecewise function with curve, line, and square root segments

Graphing: Setting Window Parameters

  1. Press ◆ semicolon, then F1 to open the Y= editor.

  2. Input the function, with x as the variable.

    Calculator screen showing the function y1 = x³ - 30.x + 15

  3. Press ◆ semicolon, then F2 to input window settings.

    Graph of piecewise function with three distinct segments.

  4. Press ◆ semicolon, then F3 to display the graph.

    Graphing calculator screen displaying a vertical line graph with menu options at the top

  5. If necessary, repeat Step 3 to adjust the window settings to get a better view of the graph and then repeat Step 4 to display the graph.

    Graphing calculator window settings showing x-range from -10 to 10 and y-range from -100 to 100 Graphing calculator screen displaying a curved graph with one peak and one trough, resembling a cubic function.

Graphing: Zooming In

  1. Press ◆ semicolon, then F1 to open the Y= editor.

  2. Input the function or functions that you wish to graph, with x as the variable.

    Graphing calculator function editor showing equations: y₁ = x², y₂ = x²·sin(1/x), and y₃ = -x².

  3. Press ◆ semicolon, then F2 to input window settings.

    Graphing calculator window settings showing Xmin = -1, Xmax = 1, Ymin = -1, Ymax = 1.

  4. Press ◆ semicolon, then F3 to display the graph.

    Graphing calculator display showing multiple intersecting curves, likely a graph of rational or asymptotic functions

  5. Press F2 to open the zoom menu and scroll down to Two colon zoom in.

    Graphing calculator showing Zoom menu with 'Zoom In' option highlighted over a plotted graph.

  6. Press the Enter key as many times as desired to zoom in on graph.

  7. Press ◆ semicolon, then F3 to display the graph.

    Graphing calculator screen displaying multiple mirrored rational functions forming symmetrical curves centered on the y-axis.

Graphing: Improving Appearance

  1. Press ◆ semicolon, then F1 to open the Y= editor.

  2. Input the function, with x as the variable.

    Graphing calculator equation entry screen with the function y1=tan⁡(x)y_1 = \tan(x)y1=tan(x) selected for plotting.

  3. Press ◆ semicolon, then F3 to display the graph.

    Graphing calculator screen displaying the graph of y=tan⁡(x)y = \tan(x)y=tan(x) with characteristic vertical asymptotes and repeating wave-like patterns.

  4. To improve the appearance of the graph, first press ◆ semicolon, then F1 to open the Y= editor.

  5. Press second, then F1 to open the style menu. Scroll down to 2 colon dot and press the Enter key.

    TI graphing calculator screen showing y1 = tan(x) with the F6 Style menu open and '2:Dot' selected.

  6. Press ◆ semicolon, then F3 to display the graph.

    Graphing calculator screen showing the graph of y=tan⁡(x)y = \tan(x)y=tan(x) plotted in dot style, resulting in a dotted curve with visible breaks at vertical asymptotes.

Least-Squares Curve Fitting

  1. Press Applications, then scroll to data divided by Matrix Editor.

    Graphing calculator home screen displaying app icons such as Contacts, Data/Matrix, EEPro, Finance, Graph, and Home, with the Data/Matrix Editor highlighted.

  2. Press the Enter key. Scroll down to Three colon new.

    Graphing calculator screen showing 'Data/Matrix Editor' menu with options: 1: Current, 2: Open..., 3: New...

  3. Press the Enter key. Scroll down to the variable: field, and input a name for the new data variable (for example, c).

    Graphing calculator screen showing 'NEW' Data/Matrix Editor setup with fields for Type (Data), Folder (main), and Variable (c), plus Enter=OK and ESC=Cancel options.

  4. Press the Enter key twice. Input the values of the independent variable in column c1, and input the corresponding values of the dependent variable in column c2.

    Graphing calculator screen displaying a data table with three columns (c1, c2, c3) and four rows of numeric values

  5. Press F5. Press ► semicolon to select a Calculation Type and scroll down to 5 colon linereg.

    Graphing calculator screen showing a menu titled 'Calculate' with various regression options; '5: LinReg' (Linear Regression) is highlighted.

  6. Press the Enter key twice. Input c1 in the x field and c2 in the y field.

    Graphing calculator screen displaying a linear regression setup with X set to column c1 and Y set to column c2.

  7. Press the Enter key to calculate the slope a and y-intercept b of the best-fitting line for the data.

    Graphing calculator screen showing linear regression statistics (y = a·x + b) with values for a, b, correlation (corr), and R²

Visualizing Limits

  1. Press ◆ semicolon, then F1 to open the Y= editor.

  2. Input the function whose limit you wish to visualize, with x as the variable.

    Graphing calculator screen displaying the function y1(x)=x2+4−2x2y_1(x) = \frac{\sqrt{x^2 + 4} - 2}{x^2}y1(x)=x2x2+4−2 entered for plotting

  3. Press ◆ semicolon, then F2 to input window settings. Be sure the interval of x-values for the viewing window includes the value that the independent variable approaches in the limit.

    Graphing calculator window settings showing values for Xmin, Xmax, Ymin, Ymax, and scale/resolution parameters.

  4. Press ◆ semicolon, then F3 to display the graph.

    Graphing calculator display showing a plotted graph with horizontal and vertical axes, and a curve approaching a horizontal asymptote.

  5. Press ◆ semicolon, then F2 to input new window settings.

    Graphing calculator window settings with very small X-axis values (e.g., Xmin = –1×10⁻⁵, Xmax = 1×10⁻⁵) and adjusted Y-axis range for zooming in closely.

  6. Press ◆ semicolon, then F3 to display the graph in the new viewing window. Use caution when trying to determine the value of a limit by inspecting graphs of a function. This may or may not lead to a correct guess for the limit, depending on the viewing window specified for each graph.

    Graphing calculator display showing a zoomed-in plot with sharp oscillations near the y-axis, indicating rapid changes or a discontinuity around x = 0.

Predicting Limits

  1. Press ◆ semicolon, then F1 to open the Y= editor.

  2. Input the function whose limit you wish to predict, with x as the variable.

    Graphing calculator screen displaying the function y1(x)=1−cos⁡(x)/x entered for plotting.

  3. Press ◆ semicolon, then F2 to input the window settings.

    Graphing calculator window settings showing Xmin = –5, Xmax = 5, Ymin = –2, Ymax = 2, with scale and resolution values set for standard zoom.

  4. Press ◆ semicolon, then F3 to display the graph.

    Graphing calculator display showing the plot of a smooth curve crossing the origin

  5. Press ◆ semicolon, then F4 to display the TABLE SETUP dialog box.

    Graphing calculator screen displaying the Table Setup menu with TblStart set to 0 and ΔTbl set to 1, along with graph-to-table and independent variable options.

  6. Scroll down to the independent field. Press ► semicolon and scroll to down to 2 colon ask. Press the Enter key.

    Graphing calculator screen showing the Table Setup menu with options for tblStart, triangle tbl, Graph<->Table, and Independent variable settings.

  7. Press ◆ semicolon, then F5 to display the table. Input values in the x column that approach the value that the independent variable approaches in the limit. The calculator will generate corresponding values of the function in the y1

    Graphing calculator screen showing a data table with values of x and corresponding y1 outputs, including entries like 0.1 → 0.04996 and 0.01 → 0.005.

Finding Roots of an Equation of the Form f(x)=0

  1. Press ◆ semicolon, then F1 to open the Y= editor.

  2. Input the function, with x as the variable.

    Graphing calculator screen displaying the function editor with the equation y₁ = x⁵ + 9x - 4 entered and active; other function slots (y₂ to y₇) are empty.

  3. Press ◆ semicolon, then F2 to input the window settings.

    Graphing calculator screen showing window settings: x-range from -3 to 3, y-range from -200 to 200, with x-scale set to 1 and y-scale set to 50.

  4. Press ◆ semicolon, then F3 to display the graph.

    Graphing calculator display showing the plot of a smooth curve crossing the origin

  5. Press F5 to open the Math menu, and scroll down to 2 colon Zero.

    Graphing calculator screen showing a graph with a function plotted and the Math menu open, highlighting the “Zero” option to find x-intercepts.

  6. Press the Enter key.

    Graphing calculator screen showing the function graph with a prompt for “Lower Bound?” while finding a zero; cursor is at x = 0, y = –4.

  7. Press ◄ semicolon as many times as desired to move to any position to the left of the desired root, which is an x-intercept on the graph. This is the lower bound of the interval for x.

    Graphing calculator screen showing a graph with the “Lower Bound?” prompt for finding a zero; cursor positioned at approximately x = –0.56962, y = –9.18655.

  8. Press the Enter key to set the lower bound chosen in Step 7.

  9. Press ► semicolon as many times as desired to move to any position to the right of the desired root. This is the upper bound of the interval for x.

    Graphing calculator screen showing the “Upper Bound?” prompt for finding a zero; cursor is positioned at approximately x = 1.55696, y = 19.162.

  10. Press the Enter key to set the upper bound chosen in Step 9. The calculator will display the root of the equation that occurs within the specified interval for x.

    Graphing calculator screen displaying the result of finding a zero; the function intersects the x-axis at approximately x = 0.442558, where y = 0.

Evaluating a Definite Integral

  1. From the calculator Home screen, press second, then Seven to input integral left parenthesis.

  2. Input the integrand function, then a comma, input the variable of integration, then a comma, input the lower limit of integration, then a comma, input the upper limit of integration, and then input a right parenthesis.

    TI graphing calculator screen with an integral expression being entered

  3. Press the Enter key to evaluate the integral.

    This image shows the result of evaluating the definite integral

Graphing Parametrically Defined Curves

  1. Press mode, select the Graph field, and press ► semicolon.

  2. Scroll down to 2 colon PARAMETRIC and press the Enter key.

    This image shows the MODE settings with PARAMETRIC selected from a TI-89

  3. If necessary, change the Angle mode to the units (RADIAN or DEGREE) you want to use for t.

  4. Press the Enter key again to save the settings and exit the MODE dialog box.

  5. Press ◆ semicolon, then F1 to open the Y= editor.

  6. Input the desired parametrized formulas for x and y into the xt1 and yt1 fields, respectively, with t as the variable.

    This image shows the parametric graph entry screen xt1 = 3. sin(5.t), yt1=2.cos(3.t)

  7. Press ◆ semicolon, then F2 to input window settings.

    This image shows the Window Settings screen for Parametric Mode on a TI-89 (or similar) calculator

  8. Press ◆ semicolon, then F3 to display the graph.

    This is a Lissajous curve, created by combining sine and cosine waves with different frequencies

  9. When you are finished graphing parametrically defined curves, press mode and set the Graph mode back to 1 colon FUNCTION.

Graphing Polar Equations

  1. Press mode, select the Graph field, and press ► semicolon.

  2. Scroll down to 3 colon POLAR and press the Enter key.

    This image again shows the MODE screen on a TI-89 calculator, with Option 3: PLOAR highlighted

  3. If necessary, change the Angle mode to the units (RADIAN or DEGREE) you want to use for θ.

  4. Press the Enter key again to save the settings and exit the MODE dialog box.

  5. Press ◆ semicolon, then F1 to open the Y= editor.

  6. Input the expression for r, with θ as the variable.

    This image shows the Polar Graph Entry screen on a TI-89 calculator

  7. Press ◆ semicolon, then F2 to input window settings.

    This image shows the window settings for Polar mode on a TI-89 (or similar) calculator

  8. Press ◆ semicolon, then F3 to display the graph.

    This image shows the graph of the polar equation:r(θ)=1+cos(θ)

  9. Press F2 to open the zoom menu, and scroll down to A colon ZoomFit.

    This image shows the Zoom settings with A: ZoomFit selected from a TI-89

  10. Press the Enter key.

    This image shows the graph of the polar equation:r(θ)=1+cos(θ)

  11. When you are finished graphing polar equations, press mode and set the Graph mode back to One colon FUNCTION.

Graphing Conic Sections in Cartesian Coordinates

  1. From the calculator Home screen, press F2, then the Enter key to input solve left parenthesis.

    This image again shows the Algebra screen on a TI-89 calculator, with Option 1: solve( highlighted

  2. Input the Cartesian equation of the conic section, then a comma, then y, and then a right parenthesis.

    The image shows a TI graphing calculator with the following equation being solved:solve(x^2 - 6x + 2y^2 + 8y = 3, y)

  3. Press the Enter key.

    This image shows the solution to the equation: x² - 6x + 2 y² + 8y = 3

  4. Press ◆ semicolon, then F1 to open the Y= editor. Input the two solutions found in Step 3 into the y1 equals and y2 equals fields. (Note that if the conic section is a parabola that opens up or down, then there will be only one solution to input into the y1 equals field.)

    The image is of a graphing calculator screen (likely a TI-89 or similar), showing two mathematical functions

  5. Press ◆ semicolon, then F2 to input window settings.

    This image shows the window settings of a graphing calculator, which define the visible region of the graphing screen

  6. Press ◆ semicolon, then F3 to display the graph.

    This image shows the graph of a conic section, specifically an ellipse, displayed on a TI calculator.