# Instructions for Our Graphing Software

Our graphing software, including our graphing calculator and other graphers on this site, can easily graph functions, equations, parametric curves and point sets. Simply type the expression into any expression box, and the software will automatically detect the type of expression and generate the graph in real-time (default) using the Cartesian or Polar coordinate systems. You can easily switch between them by selecting/deselecting the Polar checkbox. The software is designed to automatically adjust the variables according to the expression type and coordinate system, so you don't have to worry about which variable (x, y, t, or θ) to use.

Our graphing software is designed to be intelligent and user-friendly. When you enter a function using x as its variable, the expression label will automatically display "f(x) =" or "f(θ) =", depending on the selected coordinate system. If your expression contains an equal sign ("="), the software will switch to equation mode and display "Eq:" in the expression label. If your expression contains both commas and semicolons, the software will switch to points mode and display "x, y;" or "r, θ;", depending on the coordinate system. If your expression contains a comma, the software will switch to parametric mode and display "p(t) =" in the expression label, replacing all x's in the expression with t's. If you delete the comma, the software will switch back to function mode and replace all t's with x's or θ's, depending on the coordinate system. To see these changes, simply click anywhere on the calculator.

• 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.
Tips - As you type:
• pi is replaced by π,
• inf (infinity) is replaced by , and
• ..t is replaced by θ. Also see Syntax.

To graph piecewise defined functions or piecewise defined parametric curves type in each piece with the corresponding subinterval as a single function or single parametric expression.

The quickest way to type dom=(0, 2π) or dom=(-∞, ∞) is by deleting the domain entirely, including dom=.

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.

MosuseMatics! This interactive graphing software, which utilizes the most sophisticated Cartesian and polar coordinate systems, allows you to use your mouse to perform unique operations, as outlined below:

• Click on or near an axis and move your mouse to rotate the axis. The graphs are re-drawn to reflect the rotated axes. Click again to release the axis.
• Hold down the Alt key and click on an axis to change the scale (zoom in one direction). The point that was clicked will be labelled "1" (or "-1") and becomes the new unit for that axis.

Also:

• Drag the mouse to move the coordinate system and the graphs together.
• Double-click on the canvas to move the origin to the location where you clicked.

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.

You can access the following options by clicking on the ⚙ (gear) button located in the top right corner of the graph canvas:

• Change the thickness of the graphs using the provided slider.
• Select the angle mode (radians - default, degrees, or grades).
• Deselect the Graph As You Type option if you do not want the graphs to update automatically when interacting with the graphing software, including typing, mouse operations, and clicking a button. In this case, you will need to press the Graph Selected Expressions button, which will appear at the bottom of the calculator, to update the graphs manually.
• Optionally display controls at the top of the graphing software that enable you to animate rotation of any or all axes.
• The graphing software remembers and retrieves expressions you enter between visits. You can clear them by pressing the Reset Calculator button.