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.

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) = cos^{2}(x) - sin^{2}(x)

To find the **roots** 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 **x ^{2} - 3x + 2 = 0**, just type in the left hand side and press

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 x^{10} 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.

Tip: As you type:

**pi**is replaced by**π**,**inf**(**infinity**) is replaced by**∞**, and**..t**is replaced by**θ**— (this is applicable to Polar Function Grapher. The**Graphing Calculator**intelligently replaces variables by suitable ones. Also see Syntax).

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.

You can also use Polar Function Grapher, Parametric Grapher and Polar Parametric Grapher to instantly graph commonly used expressions and animate the graphing process.

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.).- Select the angle mode (
**radians**—*default*,**degrees**or**grades**).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 mouseIn 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.