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Inserting a Cartesian Graph
The graph pictured is a representation of y = e^x.
- Position the cursor at the location where you want to insert the graph.
- Click Insert from the menu bar, mouse over Graph and select Cartesian.
A cartesian graph with default properties is inserted, and the Format Graph – Cartesian window opens.
The Functions tab lets you add, edit, and delete items from the graph. These items include f(x), f(y), Parabola, Circle, Ellipse, Hyperbola, Point(x, y), Segment, Polynomial, Parametric, Normal Curve, Picture, Shape, Pie Chart, Text Box, and Compound.
The Axes tab lets you change attributes of the horizontal and vertical axes such as the scale (units per tick), ticks per inch, and line styles.
The View tab lets you change the size and background of the graph, and whether it is centered on a certain value or anchored at the lower left to a certain value.
- Click the Functions tab, select the type of item you want to add from the drop-down menu and click New.
- To edit existing items, select the description of the item and click Edit (or double-click the description).
- To delete an item, select the description of the item and click Delete.
- To change the order of the items on the graph, click the item you want to reorder and drag it to the correct position.
- Click the Axes tab, enter labels for the horizontal and vertical axes or choose to leave the labels blank. By default, the labels are x and y. Click Font to set the font characteristics of the labels. The font characteristics used for the axes labels are also used for the tick labels.
NOTEVariables cannot be used as values for the axes labels, units per tick, ticks per inch, ticks per label, width, height, or baseline. Variables can be used to define most of the attributes for the items added to the graph.
- Set the scale (units per tick) for the each axis. Units per tick must be greater than zero.
- Set the ticks per inch for each axis. Values must be between 1 and 50.
- Set the ticks per label for each axis. Values must be between 1 and 99.
- Set each axis width. You can hide the axes altogether, or display each axis with a thin or a thick line.
- Set the axis colors. To change the color of the axes labels or the tick mark labels, click Font.
- By default, each axis displays tick marks and tick-mark labels. To show or hide these click the Show tick marks and Label tick marks check boxes.
- Click Zoom In or Zoom Out to quickly change the units per tick for both axes. Zooming in or out automatically applies changes to the graph.
- Click Clear to remove the axes labels, tick marks, tick mark labels, and background. This is useful if you are using the graph to display a picture or shape.
- Click the View tab, enter a width, height, and baseline (in inches) for the graph.
- Select a background style for the graph. The background can be blank, dotted, or lined. If you select a lined or dotted background, you can also choose a color. By default, the background is blank. Lined or dotted backgrounds help define the coordinate system.
- Set the center or the lower left of the graph. Enter x, y coordinate values in the appropriate section.
- Click the Web tab to enter alternate text to be displayed when the student points to the graph while taking an internet or LAN-based test.
- Click Apply to view your changes in the editing window or click OK to record your changes and close the Format Graph – Cartesian window.
TIPIf you inadvertently apply changes that you do not want to the graph, close the Format Graph – Cartesian window, click Edit from the menu bar and select Undo Graph Change. This will cancel all changes made while the window was displayed, including inserting new items.
f(x) or f(y)
- Insert a Cartesian graph into a question, answer, matching group, rationale, feedback, or narrative.
To edit an existing graph, double-click the graph or click Format from the menu bar and select Format Graph.
- Click the Functions tab, select f(x) or f(y) from the drop-down menu and click New.
- Enter a function using x or y as the variable. The example shown above shows the function sin(x). Use the same algorithmic syntax used to define variables.
- Select a relation from the drop-down menu: equals, less than, less than or equal to, greater than, or greater than or equal to.
The relation determines the line style for the function as well as whether the area above or below the function is shaded.
- Enter the domain of the function. The default domain for functions of x or y is from -inf(infinity) to inf(infinity).
- Optionally, to display the function only if a certain condition is met, enter the condition in the field following Display function (only if).
- To change the drawing style for the function, click the Pattern drop-down menu .
- To change the color of the function, click the Color drop-down menu .
- To change the style for the shaded region, click the Shading drop-down menu . If the relation is "=", the shading style is not used.
- Click Apply to view your changes in the editing window or click OK to record your changes and close the New Function window.
NOTEVariables can be used anywhere in the function definition or as values for the domain. Click the Add from List button next to the function definition to display a list of currently defined variables, constants, and keywords.
Parabola
- Insert a Cartesian graph into a question, answer, matching group, rationale, feedback, or narrative. To edit an existing graph, double-click the graph or click Format from the menu bar and select Format Graph.
- Click the Functions tab, select Parabola from the drop-down menu and click New.
- Select a parabola type. The parabola can be open horizontally or vertically, and have the vertex on the origin or on an arbitrary point.
- Select a relation from the drop-down menu: equals, less than, less than or equal to, greater than, or greater than or equal to.
The relation determines the line style for the parabola as well as whether the area above or below the parabola is shaded.
- Enter a value for a (the distance between the vertex and the focus).
NOTEVariables can be used as values for the distance between the vertex and the focus and the vertex coordinates.
- Enter values for h and k (vertex), if the vertex is not on the origin.
- Enter the domain of the parabola. By default, the domain is from -inf(infinity) to inf(infinity).
- Optionally, to display the parabola only if a certain condition is met, enter the condition in the field following Display parabola (only if).
- To change the drawing style for the parabola, click the Pattern drop-down menu .
- To change the color of the parabola, click the Color drop-down menu .
- To change the style for the shaded region, click the Shading drop-down menu . If the relation is "=", the shading style is not used.
- Click Apply to view your changes in the editing window or click OK to record your changes and close the New Parabola window.
Circle
- Insert a Cartesian graph into a question, answer, matching group, rationale, feedback, or narrative.
To edit an existing graph, double-click the graph or click Format from the menu bar and select Format Graph.
- Click the Functions tab, select Circle from the drop-down menu and click New.
- Select a circle type. The circle can be centered on the origin or on an arbitrary point.
- Select a relation from the drop-down menu: equals, less than, less than or equal to, greater than, or greater than or equal to.
The relation determines the line style for the circle as well as whether the area inside or outside the circle is shaded.
- Enter a value for r (the radius).
NOTEVariables can be used as values for the radius and the center point.
- Enter values for h and k (the center) if the circle is not centered on the origin.
- Optionally, to display the circle only if a certain condition is met, enter the condition in the field following Display circle (only if ).
- To change the drawing style for the circle, click the Pattern drop-down menu .
- To change the color of the circle, click the Color drop-down menu .
- To change the style for the shaded region, click the Shading drop-down menu . If the relation is "=", the shading style is not used.
- Click Apply to view your changes in the editing window or click OK to record your changes and close the New Circle window.
Ellipse
- Insert a Cartesian graph into a question, answer, matching group, rationale, feedback, or narrative.
To edit an existing graph, double-click the graph or click Format from the menu bar and select Format Graph.
- Click the Functions tab, select Ellipse from the drop-down menu and click New.
- Select an ellipse type. The ellipse can be centered on the origin or on an arbitrary point.
- Select a relation from the drop-down menu: equals, less than, less than or equal to, greater than, or greater than or equal to.
The relation determines the line style for the ellipse as well as whether the area inside or outside the ellipse is shaded.
- Enter values for a (semi-major axis) and b (semi-minor axis).
- Enter values for h and k (the center) if the ellipse is not centered on the origin.
- Optionally, to display the ellipse only if a certain condition is met, enter the condition in the field following Display ellipse (only if ).
- To change the drawing style for the ellipse, click the Pattern drop-down menu .
- To change the color of the ellipse, click the Color drop-down menu .
- To change the style for the shaded region, click the Shading drop-down menu . If the relation is "=", the shading style is not used.
- Click Apply to view your changes in the editing window or click OK to record your changes and close the New Ellipse window.
Hyperbola
- Insert a Cartesian graph into a question, answer, matching group, rationale, feedback, or narrative. To edit an existing graph, double-click the graph or click Format from the menu bar and select Format Graph.
- Click the Functions tab, select Hyperbola from the drop-down menu and click New.
- Select a hyperbola type. The hyperbola can be open horizontally or vertically, and centered on the origin or on an arbitrary point.
- Select a relation from the drop-down menu: equals, less than, less than or equal to, greater than, or greater than or equal to.
The relation determines the line style for the hyperbola as well as whether the area inside or outside the curves is shaded.
- Enter values for a (semi-major axis) and b (semi-minor axis).
NOTEVariables can be used as values for the semi-major axis, the semi-minor axes, the center point, and the domain.
- Enter values for h and k (the center) if the hyperbola is not centered on the origin.
- Enter the domain of the hyperbola. By default, the domain is from -inf(infinity) to inf(infinity).
- Optionally, to display the hyperbola only if a certain condition is met, enter the condition in the field following Display hyperbola (only if ).
- To change the drawing style for the hyperbola, click the Pattern drop-down menu .
- To change the color of the hyperbola, click the Color drop-down menu .
- To change the style for the shaded region, click the Shading drop-down menu . If the relation is "=", the shading style is not used.
- Click Apply to view your changes in the editing window or click OK to record your changes and close the New Hyperbola window.
Point (x, y)
- Insert a Cartesian graph into a question, answer, matching group, rationale, feedback, or narrative.
To edit an existing graph, double-click the graph or click Format from the menu bar and select Format Graph.
- Click the Functions tab, select Point(x,y) from the drop-down menu and click New.
- Enter coordinates for the point.
NOTEVariables can be used as values for the coordinates and the label.
- Select a point style. The point style can be none, solid, or hollow.
- Select a label style. You can have no label, use the coordinates of the point as the label, or optionally enter a text label. Click Font to set the font characteristics for the label.
- Select a label position. You can select where the label will appear in relation to the point.
- To display the point only if a certain condition is met, enter the condition in the field following Display point (only if ).
- To change the color of the point, click the Color drop-down menu . To change the color of the label, click Font.
- Click Apply to view your changes in the editing window or click OK to record your changes and close the New Point window.
Segment
- Insert a Cartesian graph into a question, answer, matching group, rationale, feedback, or narrative.
To edit an existing graph, double-click the graph or click Format from the menu bar and select Format Graph.
- Click the Functions tab, select Segment from the drop-down menu and click New.
- Enter the endpoint coordinates for the line segment.
NOTEVariables can be used as values for the endpoints and the labels.
- For each endpoint, you can select a point style, label style, and label position.
- To display the segment only if a certain condition is met, enter the condition in the field following Display segment (only if ).
- To change the drawing style for the segment, click the Pattern drop-down menu.
- Click the Color drop-down menu to change the color of the segment and the endpoints.
- To change the color of the labels, click Font.
- Click Apply to view your changes in the editing window or click OK to record your changes and close the New Segment window.
Parametric Function
Parametric equations provide a convenient way to represent curves on a cartesian graph. With a parametric equation, x and y are both determined as a function of a third independent variable ( t ). The following graph shows x = f(t)= 4 * cos(t) and y = g(t) = 4 * sin(t). The domain of the function is from 0 to 2 * pi.
- Insert a Cartesian graph into a question, answer, matching group, rationale, feedback, or narrative. To edit an existing graph, double-click the graph or click Format from the menu bar and select Format Graph.
- Click the Functions tab, select Parametric from the drop-down menu and click New.
- Enter functions for x = f(t) and y = g(t) using t as the variable. Use the same algorithmic syntax used to define variables.
- Enter the domain of t. By default, t will range from –20 to +20.
NOTEVariables can be used anywhere in the function definition or as values for the domain.
Click the Add from List button next to the function definitions to display a list of currently defined variables, constants, and keywords.
- Optionally, to display the functions only if a certain condition is met, enter the condition in the field following Display function (only if).
- To change the drawing style for the function, click the Pattern drop-down menu .
- To change the color of the function, click the Color drop-down menu .
- Click Apply to view your changes in the editing window or click OK to record your changes and close the New Parametric Function window.
Normal Curve
- Insert a Cartesian graph into a question, answer, matching group, rationale, feedback, or narrative. To edit an existing graph, double-click the graph or click Format from the menu bar and select Format Graph.
- Click the Axes tab, choose to hide the tick marks and the tick-mark labels for both the horizontal and vertical axis. In the example, the label for the vertical axis was changed to P(x) and the font for the horizontal axis was changed to regular.
- Click the View tab, select Set graph left and change the x coordinate to –5.
- Click the Functions tab, select Normal Curve from the drop-down menu and click New.
- Enter the mean and standard deviation for the curve. If you want the vertical axis to go through the mean, leave the mean value set to zero.
NOTEVariables can be used as values for the mean, standard deviation, shading limits, and scaling factor.
- Optionally, for the shade part of the normal curve, select the option to shade curve from and enter the lower and upper limits as a multiple of the standard deviation. In the example, the standard deviation was set to 1, and the shading was set to –1 s to 1 s.
- Enter the scaling factor. This is used just for display purposes. The scaling factor in the example was set to 12.
- Optionally, to display the curve only if a certain condition is met, enter the condition in the field following Display curve (only if ).
- To change the drawing style for the curve, click the Pattern drop-down menu .
- To change the color of the curve, click the Color drop-down menu .
- To change the style for the shaded region, click the Shading drop-down menu .
- Click Apply to view your changes in the editing window or click OK to record your changes and close the New Normal Curve window.
Picture
Picture files, such as bitmap and jpegs, can be added to a Cartesian graph.
- Insert a Cartesian graph into a question, answer, matching group, rationale, feedback, or narrative.
To edit an existing graph, double-click the graph or click Format from the menu bar and select Format Graph.
- Click the Functions tab, select Picture from the drop-down menu and click New.
- Click Select, navigate to the location of the picture, select it and click Open.
The default picture type is bitmap (BMP). Click the Files of type box and choose the type of picture files you want to insert. The program supports the following formats: Windows Bitmap (BMP), Graphics Interchange Format (GIF), JPEG (JPG), Macintosh PICT (PCT), Windows Metafile (WMF).
NOTEPictures inserted into a graph are required to be monochrome (black and white) or 16 color (default PC palette). If a picture is inserted that requires more colors, it will have its colors reduced to 16. It is recommended that only black and white pictures be added to graphs.
- Name your picture.
- Enter the left x and top y coordinates for the picture or shape.
- Enter the width and height of the shape.
NOTEVariables can be used for the picture name, or as values for left x, top y, width, and height.
- To have the program maintain the original aspect ratio of the picture (ratio between the width of the picture and the height). Check Lock aspect ratio. If you turn this option off, you can size the picture to have any aspect ratio you want.
- To display the picture only if a certain condition is met, enter the condition in the field following Display picture (only if).
NOTEMost of the time when you are adding a picture or a shape to a Cartesian graph, you will want to clear the axes, background, and labels after your picture is positioned on the graph. With the Format Graph – Cartesian window open, switch to the Axes tab and click Clear.
- There is a preview to see how the picture or shape will look in the graph. Click Apply to view your changes in the editing window or click OK to record your changes and close the New Picture window.
Shapes
Shapes can be added to a Cartesian graph. Over 20 shapes are available. The following shows a Cartesian graph with the axes, background, and labels cleared and with a shape named prism added to the graph.
- Insert a Cartesian graph into a question, answer, matching group, rationale, feedback, or narrative.
To edit an existing graph, double-click the graph or click Format from the menu bar and select Format Graph.
NOTEMost of the time when you are adding a picture or a shape to a Cartesian graph, you will want to clear the axes, background, and labels after your picture is positioned on the graph. With the Format Graph – Cartesian window open, switch to the Axes tab and click Clear.
- Click the Functions tab, select Shape from the drop-down menu and click New.
- Select a shape from the drop-down menu or enter the name of the shape to display on the graph. The shape will be drawn in the preview window.
- Enter the left x and top y coordinates for the shape.
- Enter the width and height of the shape.
NOTEVariables can be used for the values for shape name, left x, top y, width and height.
- To display the shape only if a certain condition is met, enter the condition in the field following Display shape (only if).
- Select a pattern, color, and shading style for the shape.
- There is a preview to see how the shape will look in the graph. Click Apply to view your changes in the editing window or click OK to record your changes and close the New Shape window.
Pie Chart
- Insert a Cartesian graph into a question, answer, matching group, rationale, feedback, or narrative. To edit an existing graph, double-click the graph or click Format from the menu bar and select Format Graph.
- Click the Functions tab, select Pie Chart from the drop-down menu and click New.
- Enter a value for the left x, top y, width, and height.
NOTEVariables can be used as values for the left x, top y, width, height, degrees, label, explode distance, starting angle, gap, and pie height.
- For each pie slice, enter a size (in degrees). Any slices beyond 360 degrees are not drawn on the screen.
- Optionally, enter a label and explode distance for any/all of your pie slices. Labels appear to the right of the pie chart. If you enter labels, be sure to set the pie chart width to an amount wide enough that the labels appear.
NOTEInvalid entries may cause your pie chart to not display. For example, keep the explode distance to a small number. A large explode distance will cause your pie to be so small that it cannot be seen.
- Optionally, change the line pattern, line color, face shading, and face color. With the default settings, each slice will have a different face color.
- Optionally, change the starting angle, gap, explode direction, pie height, and label style. Changing the pie height will give the pie a 3D appearance.
- To display the pie chart only if a certain condition is met, enter the condition in the field following Display pie chart (only if).
- Click Apply to view your changes in the editing window or click OK to record your changes and close the New Pie Chart window.
Text Box
Text boxes can be added to Cartesian graphs as labels for pictures, as labels for axes, or simply to label portions of a graph not linked to a particular point or requiring text rotation.
- Insert a Cartesian graph into a question, answer, matching group, rationale, feedback, or narrative.
To edit an existing graph, double-click the graph or click Format from the menu bar and select Format Graph.
- Click the Functions tab, select Text Box from the drop-down menu and click New.
- Enter the text to display on the graph. Click Font to set the font characteristics and color for the text.
NOTEVariables can be used to define the text, as the center x and y coordinates, or as the rotation.
- Enter the center x and y coordinates. The text will be drawn with half the text to the left of this point, half to the right, half above, and half below.
- Enter the text rotation. Leave the rotation set at zero for horizontal text, or enter the number of degrees to rotate the text (counterclockwise from the x axis). For vertical text, set the text rotation to 90 degrees.
- To display the text only if a certain condition is met, enter the condition in the field following Display text (only if ).
- Click Apply to view your changes in the editing window or click OK to record your changes and close the New Text Box window.
Compound
The compound function lets you plot a combination of inequalities. The graph pictured shows the result of combining y <= x="x" and="and" y="y">= x^2 – 4.</=>
- Insert a Cartesian graph into a question, answer, matching group, rationale, feedback, or narrative.
To edit an existing graph, double-click the graph or click Format from the menu bar and select Format Graph.
- Click the Functions tab, select Compound from the drop-down menu and click New.
To add a compound function, you must have at least two inequalities (less than, less than or equal to, greater than, or greater than or equal to) functions already added to the graph. In the example, the functions y <= x="x" and="and" y="y">= x^2 – 4 have already been added. (These functions were created with shading of None.)</=>
- A checklist is displayed showing all of the items currently added to the graph that can be combined to create a compound function. Click two or more of the existing functions.
- Optionally, to display the compound function only if a certain condition is met, enter the condition in the field following Display compound function (only if ).
- To change the color of the compound region, click the Color drop-down menu .
- To change the shading style for the compound region, Click the Shading drop-down menu .
- Click Apply to view your changes in the editing window or click OK to record your changes and close the New Compound Function window.