Add/Modify 2D Function
This dialog is used to add or modify a 2 dimensional Cartesian graph function. For more information see: 2 Dimensional Cartesian Graph.

Function Definition Tab
These fields describe the mathematical attributes of the function to be graphed.

Y=f(x)= Enter the function to be graphed here, must be a valid function definition containing only "X" variables. For more information on functions and syntax see: Mathematical Expression Rules.

Examples Graph Result
3 Horizontal Line At Y=3
x^2 Parabola
Sin(x) Repeating Sine Wave
x^3+2x^2-3x-1 Third Degree Polynomial
-Sqrt(1 - x^2) Bottom Half of Circle; Radius 1

Lower Bound (Optional) And Upper Bound (Optional) - Used to restrict the functions lower or upper domain (X value). Negative infinity is assumed if lower bound is left blank, and positive infinity is assumed if upper bound is left blank. The specified bound is always included in the graph. For example, if (lower bound = -2) and (upper bound = 3) then the plotted domain is (-2 <= X <= 3). Must be a valid constant mathematical expression (in graph units).

Attempt Positive To Negative Vertical Asymptote Fix up - Like most graphing software, MathGV plots functions by calculating a large number of points from left to right along the x-axis, and drawing lines between these points. This plotting method works great for continuous functions, but can cause incorrect results with some non-continuous functions. This option fixes errors caused by vertical asymptotes (undefined points) where the "Y" value goes to positive infinity from one side and negative infinity from the other side. With out this option an incorrect line will often be drawn through the vertical asymptote connecting the highest and lowest points on either side. This option has no effect on other asymptotes.

To see a good example of this graph "Tan(x)", or "1/(X - 1.876)" with this fix up on and off. In the second example the "- 1.876" insures that the plotting method probably will not pick and calculate the exact value of the vertical asymptote. The exact value is often picked with simple functions such as "1/X". If the exact value is, by chance, picked then that asymptote is handled properly regardless of weather this fix up is enabled.

There may be some very rare instances when this fix up can be fooled into thinking that a positive to negative infinity vertical asymptote exists when one does not exits. If this error occurs uncheck the box to disable the fix up.

Attempt Extra Drawing Accuracy Near Undefined Points - MathGV will detect undefined points in two different ways; if it happens to pick one while plotting a function, or if it is told about them with the "Special X Values to Plot" option. With this feature enabled, if MathGV detects an undefined point, it will attempt to calculate extra points very close to the undefined point. It then draws these extra accuracy points.

Properties - These settings determine the visual appearance of the function.

Special X Values to Plot Tab
MathGV will automatically pick X values to plot but, sometimes these values are not the most important values. This feature is used to specify extra points (X values) to plot such as: minimum, maximum, undefined points, and asymptotes. This feature is designed to work with the "Attempt Extra Drawing Accuracy Near Undefined Points" option.

Values Grid
The grid supports 3 methods for entering values. To see the values produced by a series click the show values button.

Single value - Enter single values in the "FirstValue" column.

Series of values - To enter a series of values use the "First Value", "Second Value" and "End Value" columns.

First Value Second Value Third Value Result
1 2 10 Integers from 1 to 10
5 4 -20 Integers from 5 to –20
0 0.25 10 One quarter fractions from 0 to 10

Function series – A function can be used to calculate a series of values. For example: the undefined points for "Tan(x)" are odd integer multiples of (Pi/2). The following example enters undefined points in 2 rows. This can also be entered in 1 row.

First Value Second Value Third Value Function of X Will Generate
1 3 101 X*(Pi/2) "1*(Pi/2)", "3*(Pi/2)" to "101*(Pi/2)"
-1 -3 -101 X*(Pi/2) "-1*(Pi/2)", "-3*(Pi/2)" to "-101*(Pi/2)"

Behavior Settings
Use these settings to explicitly tell MathGV how a function behaves at each special value. Abbreviations for these settings are displayed in the last 3 rows of the grid. The settings for the current row are displayed and edited in boxes below.

At Value, Function Behavior - This setting can be used to force a value to be undefined.

Left and Right, Side Behavior
This setting specifies how the function behaves as it approaches the value from each side.

Auto - Automatic (Use Default) - With this setting the actual plotting behavior will be controlled by the "Attempt Extra Drawing Accuracy Near Undefined Points" feature on the "Function Definition" tab.

Extr - Extra Accuracy (If Undefined) - This setting forces the same calculation as the "Attempt Extra Drawing Accuracy Near Undefined Points" feature on the "Function Definition" tab.

NoEx - No Extra Accuracy (Normal) - This setting causes MathGV to plot the value and do no extra fixups.

PosI - Draw to Positive Infinity - This setting will draw the function line to positive infinity if the value is undefined. It has no effect if the value is defined.

NegI - Draw to Negative Infinity - This setting will draw the function line to negative infinity if the value is undefined. It has no effect if the value is defined.

NotC - Not Continuous - This setting will prevent a line from being drawn to the value. This feature is very useful when plotting the greatest integer function Grint(x).