Instructions for Our Graphing Software

• To graph two or more expressions on the same Cartesian or polar coordinate system press » to display the multi-graph pane. The multi-graph pane consists of expression panels, which can be added or deleted as desired by pressing + or × on each panel, respectively. Selecting or deselecting the checkbox for any expression displays or hides the corresponding graph.
• For convenience, the graphing software appends a suitable interval, either dom = (-∞, ∞) or dom = (0, 2π) to the function or parametric expressions. The software then graphs the expressions on that specified domain. You can change the end points of the interval if desired. However, the end points must be finite for polar or parametric graphing. The graphing software will automatically change any infinities to finite values.
• The points (a₁, b₁), (a₂, b₂), ... are entered as a₁, b₁; a₂, b₂; ... That is, separate the coordinates by a comma and the points by a semicolon. The last semicolon is optional, see the note below. You can use numeric expressions such as 1/2+sin(π/3) for point coordinates.
  • To Connect the points in the focused expression box with line segments, press the Connect toggle button. You can then press it again to disconnect the points. Note: If the last point ends with a semicolon, it will be connected to the first point to form a closed polygon.
• You can Animate the polar graph of a function or parametric curves (in both Cartesian and polar coordinate systems) to watch how it is constructed.
  • This tremendously useful feature can be accessed by pressing the ► button at the bottom of the graphing software (if it is hidden, first press the Animate button).
  • This will start the animation of the polar graphing process of the function or parametric graphing process of the parametric expression in focus. The graph is drawn progressively from the initial value to the final value on the specified domain.
  • You can pause the animation by pressing ‖ or stop it by pressing Done. This will also close the animation interface. To display it again, press the Animate button at the top of the grapher.
  • The speed of the graphing animation can be changed by using the slider provided.
• The Graph Fineness drop-down list controls the accuracy of the graphs drawn by the graphing software. Higher fineness settings produce more accurate graphs, but they also take longer to draw. The default fineness setting is "Normal", which is usually sufficient for most purposes. However, if you need to see more detail in the graphs, you can select a higher fineness setting. Higher fineness settings can be useful for graphing functions that have sharp curves or cusps. Note: The graph fineness can also affect the speed of the animation of the graphing process. In general, higher fineness settings will result in slower animations.
• This graphing software can also graph in non-perpendicular Cartesian coordinate systems, where the axes can be rotated to any angle. To do this, enter the amount of angle by which you want to rotate each axis in degrees, and then press the Apply button. The software will then rotate the axes and graph the expression as specified.
• You can also label an axis with any number, mathematical constant, or numeric expression, such as π, π/2, 1+√2.
• To copy or save graphs, first press the Copy/Save graph button. An image of the graph will appear below the graphing software. You can then use your browser's capabilities to save the image or copy it to your documents.
• To evaluate a function or parametric expression, type a number or a numeric (constant) expression in the box provided. The calculator will display the calculated values with the number of decimal places specified by using the slider provided.
• The graphing calculator can be used as an equation solver to find the x-intercepts (also known as zeros or roots) of a function. To do this, enter a function f(x) and press the Solve button. The calculator will then solve the equation f(x) = 0 and display the x-intercepts on the screen.
• In addition, the graphing calculator can be used as a derivative calculator. To calculate the first and second order derivatives of functions and parametric equations, press the Derivative button. You can then graph the derivatives.

Note: Our graphing software allows you to use numerical expressions, such as π or 1+√(2), wherever you can use a literal number. This includes, for example, when specifying coordinates of a point, domain end-points, axis labels, or angles.

Remark: It's important to note that the values of trigonometric functions depend on the angle mode selected. As a result, the graphs of expressions containing trigonometric functions will, as expected, differ when changing from RAD mode (default) to other modes.

Interesting curves: You can graph any of the expressions under Interesting Graphs by clicking on it. To get the best results, you may need to select Graph Fineness as +1 or higher.