<function>

The following examples illustrate use of the <function> tag properties.

Properties

Property Examples

Property Example: Attributes as properties

The <function> attributes listed above are also accessible as properties.

Property Example: numOutputs

The numOutputs property of a function is the dimension of its range.

Property Example: formula

If a function is defined by a formula, the formula property gives that formula. If the expand or simplify attributes are used, these are applied only during evaluation , so they do not effect the formula property. To simplify or expand the formula property of a function, you should nest it inside a <math> with the appropriate attributes.

The formula property isn’t currently implemented for interpolated functions.

Property Example: latex

The latex property gives the LaTeX of the function’s formula.

Property Example: numMinima

<p>The number of minima of <m>f(x) = 
	<function name="f">x^4 - x^2</function></m> is $f.numMinima.
</p>
 
<p>The number of minima found for <m>g(x) = 
	<function name="g">cos(pi x/10)</function></m> is $g.numMinima.</p>

The property numMinima gives the number of minima calculated for a function of a single variable. By default, it looks for minima in the interval $[-100,100]$. This interval can be changed with the xscale attribute.

Property Example: minima/minimumLocations/minimumValues

<p>The minima of <m>f(x) = 
	<function name="f">x^4/4 - x^2</function></m> are $f.minima.  
	The minimum locations are $f.minimumLocations.  
	The minimum values are $f.minimumValues.</p>
 
<graph size="small">
	<shortDescription>graph of <m>f</m> with its minima</shortDescription>
	$f
	$f.minima
</graph>

The property minima gives the minima of a function of a single variable as an array of points. The property minimumLocations gives the values of the independent variable where the minima occur. The property minimumValues gives the values of the function at the minima.

By default, minima are calculated in the interval $[-100,100]$.
This interval can be changed with the xscale attribute.

Property Example: numMaxima

<p>The number of maxima of <m>f(x) = 
	<function name="f">x^2 - x^4</function></m> is $f.numMaxima.</p>
 
<p>The number of maxima found for <m>g(x) = 
	<function name="g">cos(pi x/10)</function></m> is $g.numMaxima.</p>

The property numMaxima gives the number of maxima calculated for a function of a single variable. By default, it looks for maxima in the interval $[-100,100]$.
This interval can be changed with the xscale attribute.

Property Example: maxima/maximumLocations/maximumValues

<p>The maxima of <m>f(x) = 
	<function name="f">x^2 - x^4/4</function></m> are $f.maxima.  
	The maximum locations are $f.maximumLocations.  
	The maximum values are $f.maximumValues.</p>
 
<graph size="small">
	<shortDescription>graph of <m>f</m> with its maxima</shortDescription>
	$f
	$f.maxima
</graph>

The property maxima gives the maxima of a function of a single variable as an array of points. The property maximumLocations gives the values of the independent variable where the maxima occur. The property maximumValues gives the values of the function at the maxima.

By default, maxima are calculated in the interval $[-100,100]$. This interval can be changed with the xscale attribute.

Property Example: numExtrema

<p>The number of extrema of <m>f(x) = 
	<function name="f">x^2 - x^4</function></m> is $f.numExtrema.</p>
 
<p>The number of extrema found for <m>g(x) = 
	<function name="g">cos(pi x/10)</function></m> is $g.numExtrema.</p>

The property numExtrema gives the number of extrema calculated for a function of a single variable. By default, it looks for maxima in the interval $[-100,100]$.
This interval can be changed with the xscale attribute.

Property Example: extrema/extremumLocations/extremumValues

<p>The extrema of <m>f(x) = 
	<function name="f">x^4/4 - x^2</function></m> are $f.extrema.  
	The extremum locations are $f.extremumLocations.  
	The extremum values are $f.extremumValues.</p>
 
<graph size="small">
	<shortDescription>graph of <m>f</m> with its extrema</shortDescription>
	$f
	$f.extrema
</graph>

The property extrema gives the extrema of a function of a single variable as an array of points. The property extremumLocations gives the values of the independent variable where the extrema occur. The property extremumValues gives the values of the function at the extrema.

By default, extrema are calculated in the interval $[-100,100]$. This interval can be changed with the xscale attribute.

Property Example: styleDescription/styleDescriptionWithNoun

<setup>
	<styleDefinition styleNumber="3" lineColor="green" lineStyle="dashed" lineWidth="1" />
</setup>
 
<graph>
	<shortDescription>three functions with different styles</shortDescription>
	<function name="f">sin(x)</function>
	<function name="g" styleNumber="2">2cos(x/2)</function>
	<function name="h" styleNumber="3">1 - x</function>
</graph>
 
<p>The function <m>f</m> is $f.styleDescription.  It is a $f.styleDescriptionWithNoun.</p>
<p>The function <m>g</m> is $g.styleDescription.  It is a $g.styleDescriptionWithNoun.</p>
<p>The function <m>h</m> is $h.styleDescription.  It is a $h.styleDescriptionWithNoun.</p>

Since users can override styles and so may see different colors and line styles, don’t directly refer to the colors and line styles you create. Instead, use the properties styleDescription and styleDescriptionWithNoun. With those properties, the text will change to match the displayed styles.