# Graphing A Function

### Dream Calculator Start

The Graphing & List Window offers a convenient function graphing facility, as shown below. If the Function Grapher is not displayed, select Function Graphing from the window's Chart menu.

DreamCalc Function Graphing

### Plotting a Function

To plot a function of the form y = f(x):

1. Type your function into the entry box, using "x" to specify the variable. Any prefix, such as "y=", is not necessary.
2. Specify the x-value range in the MIN and MAX boxes.
3. Press return, or enter as plot A or B, as described below.

Example:

`exp(cos(x)) - 2 * cos(4 * x) + sin(x / 12)`

Rather than hitting return to enter your function, you may designate your plot as either "A" or "B" by clicking the "Enter" drop-down button. Two plots may be shown simultaneously using this method.

The input of your expression is not case sensitive. The maximum graphing numerical range is: -1E100 < x or y < 1E100. Complex numbers are not supported in graphing.

### Graphing Functions

The following functions are recognized by the Function Grapher:

• abs
• acos
• acosh
• asin
• asinh
• atan
• atanh
• cbrt
• cos
• cosh
• DLHRS
• exp
• FRCPT
• HEAVY
• INTPT
• ln
• log10
• logB
• Ran#
• root
• SIGN
• sin
• sinh
• sqrt
• tan
• tanh
• Operators: ^, +, -, *, /, %, !
• Variables: x, t

### Graphing Angle Mode

The Function Grapher has it's own angle mode, as indicated by the radio buttons in the top right of the window. This angle mode is independent of the calculator's main angle mode. It defines the operation of the trigonometric functions when the function plot is created. When changing the angle mode, you must re-enter your function by clicking Enter.

### Specifying the Range

Prior to plotting your function, you should specify the desired range of x using the MIN/MAX range edit boxes. You may also use simple expressions in the range boxes, such as: "0.86 * PI".

Alternatively, you may specify the range as part of the function input string itself--using square brackets and a semi-colon " ; " as the separator.

For example:

`sin(x) [0; PI/2]`

DreamCalc will strip off the range values and fill out the range boxes for you when the function is entered. You must, however, specify the interval separately in the Interval or No. Points edit box (see right).

### Setting No. Points or Interval

DreamCalc needs to know how many data points to generate. You can choose how to specify this using the following radio buttons:

Specify No. Points
Allows you to specify the number of points, where the corresponding interval will be calculated automatically. Generally this option is more convenient, as you do not have to re-define the interval for every function plot. However, it doesn't offer precise control of the values generated as x-inputs to your plot.

Specify Interval
Allows you to specify an interval, giving you precise control over the x values used as input to your expression. For example, if your range is [0; 10] and you specify an interval value of 1, points will be generated at integers x = 0, 1, 2, 3... up to and including 10, or eleven points in total. If your input range and interval define a number of points greater than the maximum number of permissible points, the interval will be adjusted so as to limit the number of points.

### Error Conditions

A plot will be generated if two or more y-value points were determined--even if some y-values could not be calculated. If some points could not be calculated, DreamCalc will display a small warning message in the graphing display to indicate this. If no plot data could be generated, an applicable error is be shown.

### Output to X-Y List

When the Output to X-Y List option is checked, X-Y point data is copied to the X-Y list when the plot is generated. From the list page tab, you may then edit and export the underlying data. You may re-display the data by selecting a suitable X-Y chart from the Chart menu.

The effect of the Output to X-Y List option is to overwrite the X-Y list each time you generate a function plot. If you accidentally overwrite your list, simply go to the list page tab and click undo to recover the your original data.

### Parametric Variable

You may also use the parametric variable "t" in the function input. In this case, DreamCalc will generate a plot in parametric space.

Example:

```exp(cos(t)) - 2 * cos(4 * t) + sin(t / 12)

Suggested Range: [0; 12PI]

No. Points: 1000

This is similar to specifying a function using the x-variable, and then selecting Axes->Polar Plot. However, when the t-variable is used, a parametric plot will be rendered directly onto an X-Y grid even if the Polar Plot option is not selected. In addition, if the Output to X-Y List option is checked, plot data will be copied to the X-Y list in polar r-t form.

Use of both the x and t variables in the same input string is disallowed.

### Lengthy Calculations

Generally, plots will be generated instantly. However, lengthy functions and a high number of data points may cause DreamCalc to timeout, generating only a partial plot over the desired input range. By default, DreamCalc will timeout on graphing operations after approximately 5 seconds. You can increase this in Options Window by setting the Timeout option to a value greater than 5 seconds.

### Range Comma Separator

It was stated above that you must use semi-colon as separator when specifying a range input string. The reason for not using a comma is simply that many European users use comma as the decimal point. However, if you use a period for decimal points, you may if you wish use a comma as the separator instead of semi-colon.

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