# Instruction | Graphing

Enter and graph functions and parametric expressions using this syntax. To graph two or more functions on the same coordinate plane you may have to display the scrollable multi-graph pane by clicking » on the top left of the graph canvas. The multi-graph pane consists of expression panels, either of which can be inserted 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.

You can set the accuracy of the graphs by selecting an option from Graph Accuracy drop-down list. In general, the higher the accuracy, the longer it takes to graph expressions.

To copy or save graphs first press the Save graph button. An image of the graphs will appear below the calculator. Right-click on an image and then from the pop-up menu select the desired option.

To evaluate a function or a parametric expression type in a number or a numeric (constant) expression in the box provided; the function or parametric values are displayed automatically with the number of decimal places which can be specified by using the slider provided.

When you select Polar from the top right of the graphing canvas, the polar coordinate system will be displayed and the graphs are drawn on it. By pressing Animate you can see how polar graphs or parametric graphs are constructed. You can Pause and Run the animation by using the panel which now appears on the bottom of the Graphing Calculator. You can also change the speed of graphing animation by using the slider provided.

To find the roots or zeros of a function press the Solve button. If the function is not constant it solves the equation f(x) = 0 [or r(θ) = 0, in polar case] on a bounded interval. The solution set is the x-intercepts of the Cartesian graph of the function on the bounded interval.

Remark: This is equivalent to solving one variable equations. For example, to solve the equation x2 - 3x + 2 = 0, just type in the left hand side and press Solve.

There are trivial cases that you will find extraneous "roots" or "x-intercepts" appear because of round off error. This can happen when the graph of the function is very close to the x-axis on a sub-interval. For example, the graph of x10 is very close to the x-axis on a sub-interval about 0 which produces "unwanted roots".

It is always helpful to look at the graph when finding the x-intercepts of functions.

To solve a system of linear equations try the Linear System Solver by entering the relevant augmented matrix.

To calculate the first and second order derivatives of the highlighted function or parametric equation press the Derivative button. The calculated derivatives will be displayed. You can then press Graph f, f' or Graph f, f', f" (or Graph p, p' or Graph p, p', p" in parametric case) to graph the expression together with its first and/or second derivative(s). The Derivative Graphing Calculator inserts he expressions for the derivatives below the highlighted expression or adds to the top of input panel on the left of the calculator.

The derivative calculator instantly recognizes if a function is constant in which case it will return 0. For example, if you calculate the derivative of sin(x)^2+ cos(x)^2 you will get 0 for the function is constant (=1).

The form of the derivative calculated may look different from but equivalent to what you might expect. For example, the derivative of f(x) = sin(x)cos(x) is calculated as f'(x) = cos(x)*cos(x)+sin(x)*-sin(x) which is equivalent to f'(x) = cos2(x) - sin2(x)

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

You can set the following options by pressing the (gear) button on the top left corner of the graph canvas; a scrollable transparent or opaque pane is displayed.

• Enter the amount of angle by which you want to rotate an axis and press Apply. (When graphing using the Cartesian coordinate system, in addition to the usual rectangular coordinate systems, this Graphing Calculator is capable of graphing in parallelogramical Cartesian coordinate systems by rotating the axes.)
• Label an axis with any number (π, π/2, 1+√2, etc.).

Note: Since the values of trigonometric functions depend on the angle mode you select, the graphs of expressions containing trigonometric functions will, as expected, differ as you change from RAD mode (default) to other modes.

• Furthermore, if you deselect the Graph as you interact option, the graph as you type feature will be turned off and you will have to press Graph selected expressions, which now appears on the bottom of the calculator, to update the graphs whenever you make any changes to the expressions or coordinate plane (i.e., move the origin, rotate axes, etc.).
• Change the thickness of the graphs by using the slider provided.

MouseMatics!

Rotate Axis, Translate and Change Scale by using your mouse

In addition to inputting data — by first pressing the gear button — you can use your mouse to perform some functionality unique to this interactive graphing calculator as outlined below.

• Click on (or near) an axis and move your mouse to rotate the axis. The graph(s) are drawn in generalized (parallelogrmical) Cartesian coordinate systems. Click again to release the axis.
• Drag the mouse to move the coordinate system together with the graphs.
• Double-click in the canvas to move the origin to where was clicked.
• Hold down Alt key and click on an axis to change the scale (zoom in one direction); the point which was clicked will be labeled "1" (or "-1") and becomes the new unit for that axis.

Note: If Graph As You Interact is selected, the graphs are automatically updated when performing the above, and in general, any interaction with the graphing calculator, i.e., typing, mouse operations and clicking a button. Otherwise, you have to press Graph Selected Expressions to reflect the changes you have made.