Creating a graph with GraphFree boils down to two main steps. First, select a Plot Type and use the calculator buttons from the panel at the left to enter the data for your function(s) in the upper right hand panel. Second, select what type of grid you want to use and customize the options in the lower right hand panel.
Many of the inputs in GraphFree have a yellow background when you click inside them. These areas are designed to accept input from the calculator keyboard on the left side of the screen. You may enter data in these inputs from the keyboard as well, but using the calculator buttons helps you avoid errors. There are also some symbols, such as the subtraction operator and the square root, that should be entered using the calculator buttons because they simply aren’t available on the keyboard. If you do choose the keyboard, be sure to use capital letters for variables such as X, Y and T.
Some inputs, such as the x-axis and y-axis labels, captions, etc., do not turn yellow when you enter data. That is because they are designed to accept ordinary text from the keyboard, and the calculator buttons will not affect them.
Any of the entry areas that accepts input from calculator buttons—including xMin, xMax, etc.—will also accept mathematical expressions. For example, you may enter “5√(3)” in one of these boxes, and GraphFree will accept it as a valid entry.
You can enter up to six curves to plot simultaneously, mixing and matching Plot Types as you see fit. Just click the tabs labeled Plot 1, Plot 2, etc. to enter the data for the different plots.
The green navigation buttons on the calculator panel operate only on the data entry areas designed for calculator button input. There are three different clear buttons. The basic CLR button will clear only the input with the yellow background, i.e., the one that is currently receiving input from the calculator buttons. The CLR PLOT [#] button will clear all inputs in the currently selected plot that can accept calculator button input. The CLR ALL button will clear all such inputs in all six plots. The values selected in drop down menus or in the grid settings area are not affected.
There are nine different Plot Types you can choose from, and you can create up to six different plots simultaneously by clicking on the tabs labeled Plot 1, Plot 2, etc. The six plots do not have to be the same type. You can plot a Slope Field with an ordinary Function, a Polar graph with an XY Scatter, or any other combination that you might find useful.
This is the most commonly used type, suitable for ordinary functions of the form f(x), such as f(x) = x². All style options (Color, Width, and Line Style) are active for this type of plot.
Implicitly defined functions are functions that are not solved explicitly for a single variable. An example is x³ + 2xy + y³ = 6. The implicit functions most commonly encountered are conic sections such as circles, ellipses, and hyperbolas. To enter these equations, enter the entire equation, including the “=” symbol. (The X, Y, and = buttons will become active when you select the Implicit type.) The Line Style option is not available for the Implicit type.
Implicit plots can be a bit slow, depending on their complexity and the speed of your computer. This is because implicit plots require many times more calculations to complete than other types. GraphFree tries to work as efficiently as possible, but a side effect of the quest for speed is that details that are smaller than 6–10 pixels across may not show up well.
The Polar type is designed to graph curves in the form r = f(θ), such as r = 2sinθ. There is a Polar Grid type that you may select from the grid options panel if you wish, but you don’t have to use it. The ordinary Cartesian grid will also work fine.
You will also need to specify the smallest and largest values of θ to plot in the θMin and θMax boxes. Be sure the Angle Unit is set to the value you intend, whether degrees or radians.
In a parametric plot, x and y are functions of t. For example, x(t) = 5t; y(t) = 20 - t². A parametric plot also requires that you specify the smallest and largest values of t to plot, using the tMin and tMax boxes.
In a piecewise function, the function is comprised of different rules that apply to different parts of the domain. These parts may or may not form a continuous function.
To enter a piecewise function, enter the different branches of the function together with the appropriate conditions. You do not need to use all three rows. If you have a function with more than three conditions to consider, you may enter the first three branches in one plot (e.g., Plot 1) and the remainder of the function in another piecewise plot.
You can also include a single open or closed point in a piecewise graph (as long as you have the Show open and closed endpoint symbols box checked). To show a single closed circle at (5, 3), enter “5” for one of the function entries and 3 ≤ x ≤ 3 for its associated condition. For an open circle, use 3 < x < 3.
This provides a quick way to graph a vertical, horizontal, or a slant asymptote by completing the appropriate equation. Asymptotes graphed using the Asymptote type will always be displayed using dashed lines, as is conventional for asymptotes, even if your browser does not support dashed lines for other types of plots.
In an XY Scatter plot, individual points are graphed. You may enter as many as six ordered pairs in the form (x, y) in any one plot. If you have fewer than six ordered pairs to plot, simply leave the unused points blank. If you wish to plot more than six points, spread them out over multiple plots. For example, you can graph nine points by entering six of them in Plot 1 and the other three in Plot 2.
Remember that you can also enter mathematical expressions such as “2√(2)” for your coordinates. This can be especially useful for plotting points arising from trigonometric functions.
Slope fields are most commonly encountered in calculus courses, including those that follow the AP Calculus curriculum. The slope field will be plotted at the points where tick marks appear (or would appear if they were enabled) on their respective axes. For example, if you have xTick set to 2 and yTick set to 1, then you would see the slope field segments at the points illustrated below.
The Number Line type is designed to graph an interval (or a single point) on a number line, complete with open and closed endpoint symbols. To graph a single point, set the beginning and end of the interval to the same value. For example, to graph the single point at x = 6 use the interval 6 ≤ x ≤ 6. (This is similar to the procedure for creating a single point in a piecewise function, as illustrated above.)
You will presumably want to select Number Line for the Grid type as well when you use the Number Line Plot type. While GraphFree will allow you to use a Cartesian or polar grid with a Number Line plot, it’s unlikely that you would have a reason to do so.
GraphFree offers four different Grid type settings. While some kinds of grids are more naturally suited for certain Plot types, GraphFree will let you use any Plot type with any Grid type.
Also known as a rectangular grid, this is the most common grid selection. Select the range of x and y values you wish for the grid to cover in the boxes labeled xMin, xMax, etc. The values of xTick and yTick tell how far apart the gridlines or tick marks are, assuming that you have them selected in the Gridlines menu.
The “rad” here stands for radians. The difference between the Cartesian (rad) type and the ordinary Cartesian grid is that the Cartesian (rad) type will space the gridlines or tick marks on the x-axis in terms of pi, as you might wish to do when graphing a trigonometric function. If you choose to add labels to the axes with the Tick labels menu, the labels will also be in terms of pi. Notice that the xMin and xMax values already have the π appended to them. That means that if you want to graph over the interval 0 ≤ x ≤ 2π, you should enter “0” and “2” for xMin and xMax, not “0” and “2π”
The settings yMin, yMax, and yTick work the same way that they do in the Cartesian type.
In this type, the y-axis will use a logarithmic scale, while the x-axis remains in its standard linear form. There is no yTick option available, because the ticks or grid lines on the y-axis are automatically placed at the powers of ten.
The Polar Grid type consists of the concentric circles and radial lines typically used for graphing in polar coordinates. A polar grid will always be centered about the origin, so the only sizing option available is rMax. You can still select the spacing between circles and radial lines with rTick and θTick.
As you might expect, this is intended for use with the Number Line Plot type. Though GraphFree will not prevent you from using it with other types of plots, the results might look a bit odd.
Use this menu to choose between showing the full gridlines on your graph, just the tick marks, or neither. If you select No gridlines, then only the axes will be shown; there will be no indication of scale. If the Grid type is set to Polar, then the Tick marks only option will not be shown. Similarly, the Full grid option is removed for a Number Line grid.
Both the axes and the gridlines or tick marks (if used) will be drawn in the selected color.
Use this menu to select how many, if any, of the tick marks will contain numerical labels. If the Grid type is set to Cartesian (rad), then this menu will change to offer selections in terms of π, and the labels along the y-axis will be adjusted to appear with frequency similar to that of those along the x-axis. In this case, the choices of tick frequency available will also depend on the value selected for xTick. If xTick is set to show tick marks every π/2, for example, then the Tick labels option Every π/6 will not be available, because that would make the labels closer together than the tick marks themselves.
The font size of the labels is automatically adjusted to use smaller type when the labels are close together. For legibility reasons, however, there is a lower limit to the size of the type. If your labels are too close together to read easily, adjust this setting (or one of the Ticks settings).
This menu sets the background color of the graph; a transparent background option is included.
Use the keyboard to enter text for the axis labels, e.g., “t, seconds.”
Use the keyboard or the mouse to adjust this setting. These dimensions must be between 50 and 1000 pixels. (The 50 pixel lower limit is intended primarily for Number line graphs that do not need a large height. Other graphs that are only 50 pixels wide or high will probably not turn out as well.)
These settings include only the pixels allotted to the graph itself. If you include a caption, then the final image will be 25 pixels taller than the Plot height setting. If you include a legend, the final image will be 200 pixels wider than the Plot width.
If you are using an Implicit plot, be aware that very large graphs may take a while to render, especially if the equation involves a large number of operations.
Use this setting to choose whether trigonometric calculations are performed in radians or degrees.
This button will bring up a dialog in which you can enter text for the caption of the graph and/or a legend. The caption will be placed at the bottom of the graph, and the legend at the right side of the graph.
You do not need to fill in every blank in the dialog box. If you leave the caption blank, GraphFree will not allot space for it. Similarly, you need only fill in the legend labels for the plots you are actually using and wish to label. If you leave the labels for all six plots blank, no space will be allotted for the legend.
The Add Shading dialog provides the ability to shade above or below a curve for graphing inequalities. You can also shade the area between two curves, creating graphs for situations commonly encountered in calculus courses.
To shade the area above or below the curve for an inequality, enter the plot as an equality using the Function type; other types of plots cannot be shaded. Then open the Add Shading dialog and change the drop-down menu for the appropriate plot from No shading to Shade above or Shade below.
To graph the area between two curves, graph both curves as usual, then shade below the top line and above the bottom line. Only the region which is both below the top line and above the bottom line will be shaded.
For customized texts beyond the caption and legend, you can use the settings contained in the Set Custom Note Texts tab. You may enter text for up to six different customized notes, as well as set the color and font size for those notes.
You don’t need to worry about where the notes will be positioned right away. After you have clicked the Create Plot button to display the graph, you can then use the mouse to drag your notes into the desired position.
There are two ways to get the graphs you create from GraphFree into your word processor, presentation software, etc. The first is to save the graph to your hard drive (or flash drive, etc.) as a PNG image file, then import the image into the software of your choice. Almost all programs that use images will accept the PNG format, so this option will nearly always work. To save a graph to your hard drive, right-click the graph and click “Save Image As” or “Save Picture as,” depending on your browser.
The other possible method is to copy and paste the graph directly from GraphFree to your word processor or other program using the clipboard. This method is sometimes much faster than saving and importing the image. Some software programs, however, require special procedures to paste images created on an HTML5 Canvas, which are the kind GraphFree creates. No matter what software you wish to paste into, you start by copying the image from GraphFree. To do this, right-click the graph and click “Copy” or “Copy Image,” depending on your browser; just be sure not to use “Copy Image Location” or “Copy image URL ” instead.
The procedure for pasting the image is sometimes as simple as right-clicking and selecting paste (or using the CTRL-V shortcut), but not always. Images created by GraphFree are generated from an HTML5 Canvas, and some software programs require slightly different procedures to paste this type of image. The procedures for pasting into several common programs are shown below. The version numbers shown are simply the versions we happened to use in our tests; it usually won’t matter if you are using a different version of the same program.
|Program||Procedure to Paste from GraphFree|
|Microsoft Word 2010||Use the “Paste Special” command from the ribbon and select “Device Independent Bitmap.”|
|Microsoft PowerPoint 2010||Select the “Paste as Picture” option. This option is available when you right click in PowerPoint’s work area or select the “Paste” drop down button from the ribbon. The keyboard shortcut CTRL-V will not work.|
|SMART Notebook 11||The standard paste operations using the keyboard shortcut CTRL-V or the “Paste” command from the menu bar work if you are using Firefox or Chrome. If, however, you are using Internet Explorer, then you will need to save the graph to your hard drive as described above and use the “Import -> Picture” command from the menu.|
|Adobe InDesign CS4||Standard pasting operations (CTRL-V, right-click and “Paste,” etc.) work.|
|Adobe Photoshop CS4||Standard pasting operations (CTRL-V, right-click and “Paste,” etc.) work.|
|OpenOffice Writer 4.1||Use the “Paste Special” command from the “Edit” menu and select “Bitmap.”|
|OpenOffice Impress 4.1||Standard pasting operations (CTRL-V, right-click and “Paste,” etc.) work.|
Quicksets save you time by letting you store and apply entire collections of settings in a single operation. GraphFree provides some built-in Quicksets, but you can also set up to four of your own custom Quicksets based on the settings you use frequently.
Whether you are using a built-in Quickset or one of your own custom Quicksets, the procedure is the same. Select your desired Quickset from the drop down menu at the bottom of the settings panel, then click the Apply Quickset button.
To add a custom Quickset with your own frequently used settings, click the Create custom Quickset button, and the options below will appear.
First select which of the four custom Quicksets (#1, 2, 3 or 4) you wish to set. If this Quickset is already in use, then your new settings for this Quickset will replace any settings already associated with that Quickset number. The menu will tell you whether or not a given numbered Quickset is already in use. You can then enter a description for your Quickset to help you identify it later. Only about the first sixty characters will be shown, so try not to make it too long.
Then you may select any number of the following checkboxes to include those settings in your Quickset. For example, if you want this quickset to produce a 200 x 200 pixel graph with a black grid on a white background and no grid line labels, you would check the boxes marked Plot width and height, Grid & background colors, and Grid lines and tick mark settings. Any settings in the groups you do not choose will be left unchanged when you apply the Quickset.
Before finishing, be sure that the settings you intend to include are set to their desired values in the regular plot and grid settings panels. That is, if you intend to create a Quickset with a 200 pixel plot width, then the Plot width needs to be set to 200 pixels now, since GraphFree creates your Quickset from the current plot and grid settings. When your settings are ready, click Create Quickset now, and the Quickset will now be included in the drop down menu of Quicksets.
Quicksets are stored on your computer in your web browser’s local storage. Most modern browsers respect this form of storage reasonably well, though GraphFree cannot promise you that your browser will always cooperate—especially if you have extremely strong privacy settings that prevent information from being stored on your computer. Since these Quicksets are stored on your own computer, you will need to set them individually on each computer you use.