The FunctionChart(f(x), x=a..b) command plots the function with qualitative information about the properties of the function f(x).  Color, arrows, fill, line thickness, line style, and various point marks are used to indicate regions of increase, decrease, upward and downward concavity, critical points, and other features.

Note:  The FunctionChart routine can be called using either the FunctionChart command or the FunctionPlot command.  They are identical commands.  Use the command name that you prefer.

Circles, diamonds and crosses are used to display the roots, extreme points and inflection points of the function.

If the independent variable can be uniquely determined from the expression, the parameter x need not be included in the calling sequence.

Property Descriptions

To describe the characteristics with which a property is plotted, the following property descriptions can be used.

arrow

Display the regions where the property is positive with arrows pointing up and regions where the property is negative with arrows pointing down.

color(poscolor, negcolor)

Plot the function with the color poscolor where the property is positive, and negcolor where the property is negative. For more information on plot colors, see plot/color.

filled(poscolor, negcolor)

Plot the function with a fill colored poscolor where the property is positive, and negcolor where the property is negative. For more information on plot colors, see plot/color.

linestyle(posstyle, negstyle)

Plot the function with a line style posstyle where the property is positive, and negstyle where the property is negative, where negstyle and posstyle are chosen from solid, dash, dot, and dashdot.

thickness(posthick, negthick)

Plot the function with a thickness posthick where the property is positive, and negthick where the property is negative, where negthick and posthick are chosen from 0, 1, 2, and 3.

The opts argument can contain any of the Student plot options or any of the following equations that set plot options.

arrowoptions = list

Options which are passed to the plots[arrow] command when plotting arrows. For more information on valid options, see plots[arrow].

concavity = property description or list of property descriptions

The concavity is shown using these properties.  By default, the concavity is shown by with arrows pointing up/down where the concavity is positive/negative and distinct fill colors also highlighting the different concavity regions. These properties are not used if they are used to display slope or sign. They can be turned off by using concavity = [].

functionoptions = list

A list of options for the plot of the function.  The options color, linestyle, and thickness are ignored if they are used to display sign, slope, or concavity.  By default the function is plotted as a colored curve with thickness equal to 1. For more information on plot options, see plot/options.

numarrows = positive integer

The number of arrows used when using arrows to display a property.

pointoptions = list

A list of options for the plot of the roots, extreme points and inflection points.  The option symbol cannot be used. For more information on plot options, see plot/options.

sign = property description or list of property descriptions

Regions where the sign of the function is positive ($0<f\left(x\right)$) and where it is negative ($f\left(x\right)<0$) are shown by these properties. By default, the sign is not shown with any property descriptions.

slope = property description or list of property descriptions

The slope is shown using these properties.  By default, the slope is shown by coloring the curve in distinct colors where the slope is positive or negative. These properties are not used if they are used to display concavity or sign. They can be turned off by using slope = [].

caption = anything

A caption for the plot.

The default caption is constructed from the parameters and the command options. caption = "" disables the default caption. For more information about specifying a caption, see plot/typesetting.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{Calculus1}\right]\right)\&colon;$

$\mathrm{FunctionChart}\left(x\exp \left(x\right)\&comma;-6..1\&comma;\mathrm{concavity}=\left[\right]\&comma;\mathrm{slope}=\mathrm{color}\left(\mathrm{red}\&comma;\mathrm{black}\right)\right)$

$\mathrm{FunctionChart}\left(\sin \left(x\right)+x\&comma;\mathrm{pointoptions}=\left[\mathrm{symbolsize}=20\right]\right)$

$\mathrm{FunctionChart}\left(\sin \left(x\right)+\frac{x}{2}\&comma;\mathrm{slope}=\left[\mathrm{thickness}\left(2\&comma;1\right)\&comma;\mathrm{linestyle}\left(\mathrm{solid}\&comma;\mathrm{dash}\right)\right]\&comma;\mathrm{concavity}=\mathrm{arrow}\&comma;\mathrm{pointoptions}=\left[\mathrm{symbolsize}=20\right]\right)$

$\mathrm{FunctionChart}\left(2x^3+1\&comma;x\&comma;\mathrm{sign}=\left[\mathrm{linestyle}\left(\mathrm{dash}\&comma;\mathrm{solid}\right)\&comma;\mathrm{color}\left(\mathrm{cyan}\&comma;\mathrm{magenta}\right)\&comma;\mathrm{filled}\left(\mathrm{coral}\&comma;\mathrm{wheat}\right)\&comma;\mathrm{thickness}\left(3\&comma;1\right)\right]\&comma;\mathrm{slope}=\left[\right]\&comma;\mathrm{concavity}=\left[\right]\right)$

$\mathrm{FunctionChart}\left(\frac{x^3-4x^2-50x+12}{x^2-x-17}\right)$