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 $\mathrm{-10}..10$ 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 $f\left(x\right)$.  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 $\left(a\,b\right)$.  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 $f\left(x\right)$ 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.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{Calculus1}\right]\right)\:$

$\mathrm{PointInterpolation}\left(\sin \left(9x\right)\,x=0..\mathrm{\pi }\right)$

$\mathrm{PointInterpolation}\left(\frac{x^2-3x+1}{x^2-4x+3}\,x=-3..4\right)$