The polynomials in question are:
Constant p(x) = 3
Linear p(x) = .5x + 3
Quadratic p(x) = .125x2 - 12
Cubic p(x) = .003125x3 - .6x
Quartic p(x) = (1/1024)x4 - .25x2 + 4
Quintic p(x) = (1/1024)x5 - (20/137)x3 + 4x
Of course 1/x graphs 1/x. The resolution is .1, so the vertical asymptotes do not display well.
Clicking 1/x will cause all polynomials to be divided by x before display. Clicking p(x)/1 returns the polynomial graphs to normal. The Tangent button displays an animation of the tangent line, The Area Button displays an animation that sweeps out the area under the curve from 0 to the right edge of the display. The Drop Button displays an animation of the horizontal and vertical drop-lines to the X and Y axes.
The Polynomial ActiveX control can be used without restriction as long as credit is given to the author. It is capable of graphing any polynomial or rational function (with integer powers of x). It is also capable of calculating the derivative of any polynomial or rational function, and displaying the tangent line at any selected point on the curve. It is capable of making area-sweeps of any section under the curve, and is capable of displaying drop-lines at any point. The resolution can be changed to enhance the display of certain curves (1/x for example). The curve can be displayed with or without axes and/or graph-paper background. Contact Peter M. Maurer at Peter_Maurer@Baylor.edu for more information.