3. Graphing and Numerical Table Creation

3-1. Basic Graphing Operations

3-1-1. To draw a graph and create a numerical table

1. Click anywhere on the Paper to display the Sticky Note menu.

2. Click to display a Graph Sticky Note.

3. At the bottom of the Graph Sticky Note, click to display a Graph Function Sticky Note.

4. Use the soft keyboard to input a function.

Example: $y = x^2$

5. On the soft keyboard, click [EXE] to display a Graph Sticky Note and draw the graph.

6. On the Graph Function Sticky Note, click to display a Graph Function Sticky Note.

3-1-2. To input a numerical table and plot it on a graph

1. At the bottom of the Graph Sticky Note, click to display a Graph Function Sticky Note.

2. Input the data values you want to plot on the Statistical Data Sticky Note.

3. Select the data value you want to input, and then on the tool palette, click [Scatter Plot].

・This draws a scatter plot.

4. At the bottom of the Graph Sticky Note, click to display a Graph Function Sticky Note.

5. Input function and graph it.

3-2. Drawing Multiple Graphs

3-2-1. To graph multiple functions

1. Click an existing Graph Function Sticky Note to select it.

2. At the bottom of the Graph Function Sticky Note, click

・This adds a new Graph Function Sticky Note.

3. Use the soft keyboard to input a function.

Example: $y = x + 2$

4. On the soft keyboard, click [EXE] to overwrite the graph.

・You can overwrite the graph as many times as you like by repeating steps 2 through 4 of this procedure.

3-2-2. To delete a particular function

1. Click the Graph Function Sticky Note to select it.

2. Click the Delete button () of the function you want to delete.

・This deletes the function.

3-3. Graphing a Rectangular Coordinate Equation ($y=, x=$)

3-3-1. To graph a y= rectangular coordinate equation (y=)

1. At the bottom of the Graph Sticky Note, click to display a Graph Function Sticky Note.

2. Use the soft keyboard to input the y= rectangular coordinate function ($y=$).

Example: $y=x^2$

3. On the soft keyboard, click [EXE] to draw the graph.

3-3-2. To graph a x= rectangular coordinate equation (x=)

1. At the bottom of the Graph Sticky Note, click to display a Graph Function Sticky Note.

2. Use the soft keyboard to input the $x=$ rectangular coordinate function.

Example: $x=3$

3. On the soft keyboard, click [EXE] to draw the graph.

3-4. Graphing a Polar Coordinate Equation ($r=$)

1. At the bottom of the Graph Sticky Note, click to display a Graph Function Sticky Note.

2. Use the soft keyboard to input the polar coordinate function.

Example: $r=5sin(3\theta)$

3. On the soft keyboard, click [EXE] to draw the graph.

3-5. Graphing a Parametric Function

1. At the bottom of the Graph Sticky Note, click to display a Graph Function Sticky Note.

2. On the soft keyboard, click .

・This displays the input format for a parametric function.

3. Input the parametric function.

Example: $x_{t}=sin(t)$  $y_{t}=cos(t)$

4. On the soft keyboard, click [EXE] to draw the graph.

Note

・You can change the range of t and draw the resulting graph.

3-6. Graphing an Inequality

1. At the bottom of the Graph Sticky Note, click to display a Graph Function Sticky Note.

2. Use the soft keyboard to input an inequality.

Example: $y>x^2-2x-6$

3. On the soft keyboard, click [EXE] to draw the graph.

Note

・Graphing is supported for inequalities expressed using the following forms: $y>f(x)$, $y<f(x)$, $y$$\geq$$f(x)$, $y$$\leq$$f(x)$.

3-6-1. To specify the shading range

You can use this procedure to specify the shading range when simultaneously graphing multiple inequalities.

1. Click the Menu button () of the Graph Sticky Note.

2. On the Inequality Plot menu, select [Union] or [Intersection].

Union ... Shades all areas where the conditions of each of the graphed inequality are satisfied.

Intersection ... Shades only areas where the conditions of all of the graphed inequalities are satisfied.

3-7. Drawing Circle, Elliptic, and Hyperbolic Graphs

3-7-1. To draw a circle graph

1. At the bottom of the Graph Sticky Note, click to display a Graph Function Sticky Note.

2. Use the soft keyboard to input a circle equation.

Example: $(x-1)^2+(y-1)^2=2^2$

3. On the soft keyboard, click [EXE] to draw the graph.

3-7-2. To draw an elliptic graph

1. At the bottom of the Graph Sticky Note, click to display a Graph Function Sticky Note.

2. Use the soft keyboard to input an elliptic equation.

Example:

$$ \cfrac{(x-1)^2}{4^2}+\cfrac{(y-2)^2}{2^2}=1 $$

3. On the soft keyboard, click [EXE] to draw the graph.

3-7-3. To draw a hyperbolic graph

1. At the bottom of the Graph Sticky Note, click to display a Graph Function Sticky Note.

2. Use the soft keyboard to input a hyperbolic equation.

Example:

$$ \frac{(x-1)^2}{2^2}-\frac{(y-1)^2}{2^2}=1 $$

3. On the soft keyboard, click [EXE] to draw the graph.

3-8. Using a List of Values to Draw Multiple Graphs

You can use a list as a coefficient in a function and simultaneously draw multiple graphs.

1. At the bottom of the Graph Sticky Note, click to display a Graph Function Sticky Note.

2. Use the soft keyboard to input a function.

Example: $y=${$1,2,3$}$x$

3. On the soft keyboard, click [EXE] to draw the graphs.

3-9. Specifying a Range to Draw a Graph

You can specify a range for drawing a graph.

To do so, input a function using the syntax below.

<function>|<inequality specifying draw range>

1. At the bottom of the Graph Sticky Note, click to display a Graph Function Sticky Note.

2. Use the soft keyboard to input a function.

Example: $y=x|-5<x<5$

3. On the soft keyboard, click [EXE] to draw the graph.

3-10. Using Trace

With trace, you can click a graph line to plot a point on it and display the coordinates at that point. You can also drag the point along the graph line.

1. Draw a graph.

Example: $y=x$

2. Click the Graph Sticky Note.

3. Click the graph to select it.

・This causes the line of the selected graph to become thicker.

4. Click the graph line to plot a point on it, and display the corresponding coordinates.

・You can also plot multiple points on the graph line.

5. Drag the point along the graph line.

3-10-1. To delete a point plotted on a graph line

1. Click the point you want to delete.

・This selects the point and displays "x" above and to the right of its coordinates.

2. Click the "×" to delete the point.

3-10-2. To use coordinate values in a calculation

1. Draw a graph.

Example: $y=x^2$

2. Click the graph line to plot a point on it.

3. Click the point again to select it.

4. At the bottom of the Graph Sticky Note, click or right-click the point.

5. Click [Show Label] to display a Coordinates Sticky Note.

・The $P_{1}$ coordinate values are stored in variables $x_{1}$ and $y_{1}$.

6. Display a Calculate Sticky Note.

7. On the Calculate Sticky Note, input the expression using the coordinates and perform the calculation.

Example: $x_{1}+y_{1}$

Note

・You can repeat steps 2 and 5 above and create multiple Coordinates Sticky Notes, if you like. If you do, the $P_{n}$ coordinate values will be stored in variables $x_{n}$ and $y_{n}$ (n = sequential number).

3-11. Basic Graph Analysis Operations

Clicking on a graph you have drawn will automatically perform appropriate analysis (for example: roots, maximum value, minimum value, directrix, axis of symmetry) depending on the graph type.

1. Draw a graph.

Example: $y=x^2-3x-2$

2. Click the Graph Sticky Note.

3. Click the Menu button ().

4. Select the [Conics] check box.

・This enables graph analysis that is characteristic of conics (directrix, axis of symmetry, focus, etc.)

5. Click the Graph Sticky Note, and then click a line of the drawn graph.

・This analyzes the graph and displays dots (●) at the analysis result coordinate points.

・The directrix and axis of symmetry are shown as broken grey lines.

6. Clicking a dot (●) will display its coordinates.

3-12. Creating a Table

3-12-1. To create a table from a function

1. Draw a graph.

Example: $y=x^2$

2. On the Graph Function Sticky Note, click to display a Table Sticky Note.

・The table generated from the function will appear in the Table Sticky Note.

3-12-2. To create a table by plotting points on a graph

1. Draw a graph.

Example: $y=x^2$

2. Click the graph line to plot points on it.

・Plot multiple points.

3. Click a plotted point to select it.

4. At the bottom of the Graph Sticky Note, click or right-click the point.

5. Click [Convert To Table] to display a Table Sticky Note.

・The coordinate values of the plotted points will be input on the Table Sticky Note.

3-13. Editing a Table

3-13-1. To add a row to a table

1. Click the Table Sticky Note.

2. Input a value in the bottom most left cell of the sticky note to add a row at the bottom of the table.

3-13-2. To delete a row from a table

1. Click the Table Sticky Note.

2. Right-click the row you want to delete.

3. Click [Delete] to delete the row.

3-13-3. To change a value in a table

1. On the Table Sticky Note, click the value you want to change.

2. Input the new value.

3-14. Using a Slider

You can change the value of a variable in a graph expression (for example, the value of a in $y=a \cdot x^2$) from the graph screen and observe how the change affects the graph.

1. Input a function that includes variables into a Graph Function Sticky Note. This will display sliders for changing the values assigned to the variables.

Example: $y= a \cdot x^2-b \cdot x \hspace{10mm} y=a \cdot x+b$

2. Click one of the arrow buttons (< or >) on either end of the slider.

・This will change the corresponding value and re-draw the graph accordingly.

Note

  • You can use a slider to change the value (variable value, lower limit value, upper limit value, step value) displayed above the slider. Click the value you want to change.
  • Clicking the arrow () below a slider starts automatic change of the variable value and re-drawing of the graph with the new values (animation). To stop the animation, click .
  • and indicate the animation playback style. indicates that playback will go left to right, and then repeat left to right. indicates that playback will go left to right, and the right to left. Click or to toggle between playback types.

3-15. Configuring Graph Display Settings

1. Click the Graph Sticky Note.

2. Click the Menu button ().

3. Configure display settings and adjust the display range.

  • Axes: Select this check box to show the coordinate axes on the graph.
    Numbered: Select this check box to show the coordinate axes and tick marks on the graph.
    Grid: Select this check box to show a grid in the draw area.
    Labels: Select this check box to show coordinate axis names on the graph.
    You can change an axis name, if you want.
    Window: Select this check box to specify a display range that is optimized for statistical data.
    X: Specifies the display range of the x-axis.
    X Scale: Specifies interval between tick marks on the x-axis.
    Y: Specifies the display range of the y-axis.
    Y Scale: Specifies interval between tick marks on the y-axis.
    Inequality Plot:   Use this procedure to specify the shading range when simultaneously graphing multiple inequalities.
    Intersection: Shades only areas where the conditions of all of the graphed inequalities are satisfied.
    Union: Shades all areas where the conditions of each of the graphed inequality are satisfied.
    Coordinates: Configures the coordinate value display setting.
    Decimal: Displays coordinate values using decimal fractions.
    Standard: Displays coordinate values using expressions.
    t: Select this check box to display parametric graph coordinate values as t values.
    ($r$, $\theta$): Select this check box to display polar graph coordinate values as $r$ and $\theta$ values.
    Conics: Select this check box to display analysis results that are characteristic of conics.

3-16. Zooming a Graph

1. Click the Graph Sticky Note.

2. Move the mouse pointer the location you want to zoom.

3. Rotate the scroll wheel of your mouse to zoom the graph.

Note

  • If you are using a tablet terminal, you can zoom by pinching in or pinching out.
  • To return to the default display, click in the lower left corner of the Graph Sticky Note.

3-17. Panning a Graph

1. Click the Graph Sticky Note.

2. Move the mouse pointer the location you want to pan.

3. Drag the graph to pan it.

Note

  • To return to the default display, click in the lower left corner of the Graph Sticky Note.

3-18. Changing the color of a Graph

1. Click the drag handle () of the Graph Function Sticky Note.

2. On the Color Palette, select the desired color to change the graph color.

3-19. Hiding a Graph

1. Draw a graph.

2. Click the drag handle () of the Graph Function Sticky Note.

3. Click [Hide].

・This hides the graph of the selected function.

・To re-display the graph, click [Show].

3-20. Displaying a Background Image

1. On the Graph Sticky Note, click .

・This displays an Image Sticky Note.

2. Click .

・This displays a dialog box for opening a file.

3. Select the image file you want and then click [Open].

4. On the Image Sticky Note, click [OK].

・This displays the image selected with the Graph Sticky Note.

・You can configure the settings below for an Image Sticky Note.

  • CenterX: Specifies the x-axis value of the image center.
  • CenterY: Specifies the y-axis value of the image center.
  • Angle: Specifies the image rotation angle.
  • Width: Specifies the image width.
  • Height: Specifies the image height.
  • Position:
    • Front・・・Displays the image in front of the coordinate axes and the grid.
    • Back・・・Displays the image in back of the coordinate axes and the grid.

Note

・Instead of performing steps 2 through 4, you can also drop the desired image file onto the Image Sticky Note.

・You can display multiple images by clicking on the Image Sticky Note.

3-21. Plot Function

3-21-1. To plot points on a graph

1. On the Graph Sticky Note, click .

・This displays a Plot Sticky Note.

2. On the Plot Sticky Note, input the x-coordinate and y-coordinate values of the points you want to plot.

・This plots points at the coordinates you input.

Note

・You can configure the settings shown below by clicking on a Dot Plots Sticky Note.

  • Plot color: Specifies the color of the plotted points.
  • Labels: Specifies the label names.
  • Lock: Locks selected cell(s). If the selected cells are locked, this item unlocks the cells.

3-21-2. To display the Coordinates Sticky Note of a point

1. Click a plotted point.

・This displays the coordinates of the Point.

2. Click the displayed coordinate values.

3. Click .

4. Click [Show Label] to display a Coordinates Sticky Note.

3-22. Inputting Text

1. On the Graph Sticky Note, click .

・This enables text input and displays the text palette.

2. Use the text palette to specify the text color and size.

3. Click the location where you want to input text and then input it.

Note

・Clicking input text selects it.

You can reposition text by dragging it.

Clicking will display the text palette, which can be used to change the color and size of the text.

To delete text, click .

・Double-clicking input text selects it for editing.

3-23. Determining the Integral Value and Area of a Region

1. Draw a graph.

2. Select the graph and then click .

3. Click "Integral".

・This displays an Integral/Area Sticky Note.

4. Input the lower limit value and upper limit value of the integration.

・This calculates the integral and area, and shades the integration.

3-24. Graph Analysis Functions

Trace
Clicking a graph line to display the coordinates at that point. You can also drag the point along the graph line.
Root (x-Intercept)
Determines the root of a graph,
and displays the point where the graph intercepts the X-axis. Click a point to show its coordinates.
Min
Determines the minimum value of a graph and displays a point at the minimum value. Click the point to show its coordinates.
Max
Determines the maximum value of a graph and displays a point at the maximum value. Click the point to show its coordinates.
y-Intercept
Determines an x-coordinate value for a y-coordinate on a graph. Displays the point where the graph intercepts the Y-axis. Click the point to show its coordinates.
Intersection
Determines the points of intersection of two graphs
and displays them. Click a point to show its coordinates.
Focus
Determines the focus of a parabolic graph, elliptic graph, or hyperbolic curve graph. Drawing one of these types of graph causes the focus to be displayed. Click the point to show its coordinates.
Vertex
Determines the vertex of a parabolic graph, elliptic graph, or hyperbolic curve graph. Drawing one of these types of graph causes the vertex to be displayed. Click the point to show its coordinates.
Directrix
Draws the directrix of a parabolic graph. Drawing a parabolic graph displays its directrix. Click the directrix to show its x-value and y-value.
Symmetry
Draws the axis of symmetry of a parabolic graph. Drawing a parabolic graph displays its axis of symmetry. Click the axis of symmetry to show its x-value and y-value.
Latus Rectum Length
Determines the length of the latus rectum of a parabolic graph. Drawing a parabolic graph displays the length of it latus rectum.
Center
Determines the center of a circle graph, elliptic graph, or hyperbolic curve graph. Drawing one of these types of graph causes the center to be displayed. Click the point to show its coordinates.
Radius
Determines the radius of a circle graph. Drawing a circle graph displays its radius. Click the radius to show its length ($r=$).
Asympotes
Draws the asympotes of a hyperbolic curve graph. Drawing a hyperbolic curve graph displays its asympotes. Click an asympote to show its equation.
Eccentricity
Determines the eccentricity of a parabolic graph, elliptic graph, or hyperbolic curve graph. Drawing one of these types of graph causes the eccentricity ($e=$) to be displayed.