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Student[Calculus1]

  

PointInterpolation

  

simplistic approximation of a function

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

PointInterpolation(f(x), x = a..b, opts)

PointInterpolation(f(x), a..b, opts)

Parameters

f(x)

-

algebraic expression in variable 'x'

x

-

name; specify the independent variable

a, b

-

algebraic expressions; specify the plot range

opts

-

equation(s) of the form option=value where option is one of functionoptions, interpolation, interpolationoptions, numpoints, output, pointoptions, showfunction, showinterpolant, showpoints, view, or Student plot options; specify options for the plot

Description

• 

The PointInterpolation(f(x), x=a..b) command plots the function f(x) and an approximation to f(x) obtained by sampling f(x) at a series of points and interpolating those points.

• 

If no range a..b is provided, the range 10..10 is used.

• 

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

• 

This routine demonstrates the failures that can result from attempting to graph an expression without finding further information about the function such as zeros, extreme points, inflection points, and asymptotes.

• 

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

  

 

  

functionoptions = list

  

A list of options for the plot of the expression fx.  By default, the expression is plotted as a solid red line. For more information on plot options, see plot/options.

  

 

  

interpolation = spline or linear

  

Whether cubic spline or linear interpolation is used to approximate the function.  By default, the value is spline.

  

 

  

interpolationoptions = list of values

  

A list of options for the plot of the interpolation. By default, the interpolation is plotted as a solid blue line. For more information on plot options, see plot/options.

  

 

  

numpoints = posint

  

The number of points evenly spaced points that span the interval a,b.  By default, the value is 6.

  

 

  

output = plot or animation

  

This option controls the return value of the function.

– 

output = plot specifies that a plot, which shows f(x), the points of interpolation, and the interpolant, is displayed.  This is the default.

– 

output = animation specifies that an animation, where the first iteration shows f(x), the next adds the interpolation points, and the third adds the interpolant, is displayed.

  

 

  

pointoptions = list

  

A list of options for the plot of the interpolating points. By default, these points are plotted as blue circles. For more information on plot options, see plot/options.

  

 

  

showfunction = true or false

  

Whether the expression fx is plotted.  By default, the value is true.

  

 

  

showinterpolant = true or false

  

Whether the interpolant is plotted.  By default, the value is true.

  

 

  

showpoints = true or false

  

Whether the interpolation points are marked.  By default, the value is true.

  

 

  

view = [DEFAULT or numeric..numeric, DEFAULT or numeric..numeric]

  

The view of the final plot.

  

 

  

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.

  

 

  

title = anything

  

A title for the plot.

  

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

Examples

withStudent[Calculus1]:

PointInterpolationsin9x,x=0..π

The command to create the plot from the Plotting Guide is

PointInterpolationx23x+1x24x+3,x=3..4

See Also

plot/options

plot/typesetting

Student

Student plot options

Student[Calculus1]

Student[Calculus1][VisualizationOverview]

 


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