I would like to announce to those using Lon-Capa for mathematics (Pitt, Purdue, Simon Fraser, et al), especially high school and first and second-year college math, that I have developed a suite of graphing questions for LC. These are not meant to replace Geogebra or FunctionPlot response questions. Geogebra is good at what it does. Given a function, it will graph it nicely. FunctionPlot response is great for plotting, say, experimental results and fitting a rough curve to data. I wanted LC questions that would turn it around: give the students a function to graph, and have the student plot critical features to create a graph, and have LC evaluate the correctness of the graph.
These questions call on libraries written using Javascript, and I have written libraries supporting the graphing of polynomials, absolute-value functions, explonential and logarithmic functions, rational functions, and trigonometric functions. Yet to come are graphers for conic sections and piecewise-defined functions. (Maybe others?) There is probably room for improvement of these questions and libraries. For example, I paid little attention to accessibility concerns. There might be browser issues with older browsers, Microsoft browswers, or mobile devices. The interface might benefit from a little tweaking. There might yet be some unexpected bugs that pop up with certain randomizations. I welcome any feedback, constructive criticism, and/or suggestions. It is my hope that one day these might be added to LC as new question types. Perhaps some enthusiastic graduate student could be employed to do this. All the required libraries and supporting files are in /res/tccfl/abertr/Graphing/ While these files are open source, I hope that no one will grab the code and port it to other LMS platforms, such as Lumen/MyOpenMath. 1. Polynomials In its general form, given n points selected by the user, with at least one point that is not an x-intercept, a degree n-1 polynomial is fit to the points using Newton's interpolating polynomial. The instructor can specify that more points than necessary be input, for example, demand that the student select 5 points for a quadratic function (if the points are on the graph correctly, then the coefficients of higher-degree terms will be 0). This same library is used for absolute value functions, but if and when I develop a library for piecewise functions, absolute value functions might better be shifted there. For samples, see /res/tccfl/abertr/CollegeAlgebra/QuadraticFunctions/QuadraticGraph01.problem through /res/tccfl/abertr/CollegeAlgebra/QuadraticFunctions/QuadraticGraph09.problem /res/tccfl/abertr/CollegeAlgebra/LinearEquations/AbsoluteValueGraph01.problem /res/tccfl/abertr/CollegeAlgebra/LinearEquations/AbsoluteValueGraph02.problem /res/tccfl/abertr/CollegeAlgebra/LinearEquations/GraphOfALine.problem /res/tccfl/abertr/CollegeAlgebra/LinearEquations/GraphOfALine02.problem /res/tccfl/abertr/CollegeAlgebra/LinearEquations/GraphOfALine03.problem For higher-degree polynomials: /res/tccfl/abertr/Precalculus/Polynomials/DrawPolyGraph01.problem /res/tccfl/abertr/Precalculus/Polynomials/DrawPolyGraph02.problem 2. Rational Functions Given a rational function P(x)/Q(x), the student will graph the function by plotting x- and y-intercepts, vertical asymptotes, and the end behavior (horozontal asymptote or other). The numerator and denominator must be polynomials, although if they are not strictly polynomials, it might still work. The zeros of the numerator and denominator must be real. P(x) and Q(x) with imaginary roots, such as x^2 + 1, is not supported (yet?). For examples, see /res/tccfl/abertr/Precalculus/PolynomialsAndRationalFunctions/graphRationalFunction01.problem through /res/tccfl/abertr/Precalculus/PolynomialsAndRationalFunctions/graphRationalFunction07.problem 3. Exponential and Logarithmic Functions Given one of these functions, the student creates the graph by plotting at least 3 points AND the asymptote, even if the asymptote is one of the coordinate axes. Incorrect graphs made by including both a horizontal and vertical asymptote, which I've seen many students do on paper, is rather crudely supported. See /res/tccfl/abertr/Precalculus/LogarithmExponential/GraphExponential01.problem through /res/tccfl/abertr/Precalculus/LogarithmExponential/GraphExponential06.problem and /res/tccfl/abertr/Precalculus/LogarithmExponential/GraphLogarithmic01.problem through /res/tccfl/abertr/Precalculus/LogarithmExponential/GraphLogarithmic05.problem 4. Trigonometric Functions The student will select the type of graph to be drawn: sine & cosine, or tangent & cotangent, or secant & cosecant. The student will then enter 5 features for each: 5 points for a wave, two asymptotes and three points for tangent and cotangent, or 3 asymptotes and two points for secant and cosecant. The student may also select the type of scale to use for the horizontal axis, either a scale labeled with rational numbers or a scale labeled with irrational numbers (multiples of pi). The selection will be driven by the period and phase shift of the given function. For examples, /res/tccfl/abertr/Trigonometry/Graphing/DrawTrigGraph01.problem through /res/tccfl/abertr/Trigonometry/Graphing/DrawTrigGraph12.problem Best regards, Rex Abert ***Due to Florida's very broad public records law, most written communications to or from Tallahassee Community College employees regarding College business are public records, available to the public and media upon request. Therefore, this email communication and your response may be subject to public disclosure.*** _______________________________________________ LON-CAPA-users mailing list LON-CAPA-users@mail.lon-capa.org http://mail.lon-capa.org/mailman/listinfo/lon-capa-users