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Function Repository Resource:

 SignChart (1.0.0) current version: 2.0.0 »

Source Notebook

Get a number line diagram with information about where a function is positive, negative, zero or discontinuous

Contributed by: Wolfram|Alpha Math Team

ResourceFunction["SignChart"][expr, x]

creates a number line diagram with information about the sign of the real univariate function expr, written in terms of the variable x.

Details

ResourceFunction["SignChart"] accepts all of the options of NumberLinePlot, as well as the following:
FontSizeMediumthe font size of sign chart labels
"PlusColor"the color corresponding to positive points/intervals
"MinusColor"the color corresponding to negative points/intervals
"ZeroColor"the color corresponding to zero or discontinuous points/intervals
TooltipTruewhether to include tooltips corresponding to critical values

Examples

Basic Examples (1) 

Get a sign chart for 2x-10, which is negative for x<5, zero at x=5 and positive for x>5:

In[1]:=
ResourceFunction["SignChart"][2 x - 10, x]
Out[1]=

Scope (1) 

Discontinuities are indicated on the sign chart with vertical dots:

In[2]:=
ResourceFunction["SignChart"][x/x^2, x]
Out[2]=

Options (4) 

FontSize (1) 

Use the option FontSize to adjust the size of labels:

In[3]:=
ResourceFunction["SignChart"][Log[x] + 1, x, FontSize -> Large]
Out[3]=

MinusColor (1) 

Use the option "MinusColor" to adjust the color of the negative intervals and minus signs:

In[4]:=
ResourceFunction["SignChart"][Log[x] + 1, x, "MinusColor" -> Red]
Out[4]=

PlusColor (1) 

Use the option "PlusColor" to adjust the color of the positive intervals and plus signs:

In[5]:=
ResourceFunction["SignChart"][Log[x] + 1, x, "PlusColor" -> Red]
Out[5]=

ZeroColor (1) 

Use the option "ZeroColor" to adjust the color of the zero or discontinuous intervals and zeros:

In[6]:=
ResourceFunction["SignChart"][Log[x] + 1, x, "ZeroColor" -> Red]
Out[6]=

Applications (1) 

Sign charts are a useful reasoning tool in many contexts, especially calculus functional analysis. For example, compare the plot of a function to the sign chart of the function's derivative to visualize the first derivative test:

In[7]:=
With[{poly = (x + 3) (x - 1) (x + 1) (x + 2)}, Column[{ Plot[poly, {x, -4, 2}, PlotRange -> {{-4, 2}, {-10, 10}}], ResourceFunction["SignChart"][D[poly, x], x] }]]
Out[7]=

Possible Issues (1) 

If there are infinitely many places where a function changes signs, the sign chart displays information for an interval surrounding x=0:

In[8]:=
ResourceFunction["SignChart"][Tan[x], x]
Out[8]=

Publisher

Wolfram|Alpha Math Team

Version History

  • 2.0.0 – 23 March 2023
  • 1.0.0 – 11 October 2022

Related Resources

Author Notes

To view the full source code for SignChart, evaluate the following:

License Information