<function>

<function> is a Math component that defines a mathematical function that can be used for numerical or symbolic evaluation, answer validation, graphing, and other computations within Doenet. There are two main ways to create a function:

1. Creating a function using a formula
2. Creating an interpolated function through given points or with specified extrema

Basic Use Examples

The following examples illustrate some of the basic uses of the <function> component.
See the following pages for more complex examples, attributes and properties.

Example: Single variable function defined by a formula

A single variable function can be defined by giving a formula in the variable $x$ as the child of <function>.
The variable can be changed with the variable attribute.

The function can be evaluated using a macro of the form $$f(x) or rendered on a <graph> using the reference $f.

Example: Vector-valued function of multiple variables

A vector-valued function can be created by giving a vector for the formula.
The variables attribute can specify multiple variables.

The macro notation $$f(x,y) can be used with multiple variables.

Example: Interpolated functions 1

To create an interpolated function, use the attributes maxima, minima, extrema, through and/or throughSlopes. The scales used in the interpolation algorithm are specified by the attributes xscale and yscale.

Example: Interpolated functions 2

Move the points
<graph size="small">
  <point name="min" labelIsName>(-8,2)</point>
  <point name="max" labelIsName styleNumber="2">(-3,6)</point>
  <point name="ext" labelIsName styleNumber="3">(4,-5)</point>
  <point name="thr" labelIsName styleNumber="4">(8,-9)</point>
  <function name="f" minima="$min" maxima="$max" extrema="$ext" through="$thr" />
</graph>
 
<ul>
<li>Minima: $f.minima</li>
<li>Maxima: $f.maxima</li>
<li>Extrema: $f.extrema</li>
<li>Minimum values: $f.minimumValues</li>
<li>Maximum locations: $f.maximumLocations</li>
</ul>

In addition to specifying extrema of functions, one can also access the actual extrema of a function with the properties: minima, minimumLocations, minimumValues, maxima, maximumLocations, maximumValues, extrema, extremaLocations, extremaValues.

These properties apply to both interpolated functions and scalar-valued functions of a single variable determined by a formula.