Getting Students to DIGMath: Dynamic Interactive Graphics in College Algebra Sheldon P. Gordon Farmingdale State College farmingdale.edu\~gordonsp

DIGMath Modules for College Algebra 1. Linear Functions (1) You can enter the slope and vertical intercept and watch the effects of changing either of them via a slider on the resulting graph. (2) You can enter a point and the slope and watch the effects of changing either of them on the graph via the point-slope formula. (3) You can enter two points and change either of them to see the effects. 2. Solving Linear Systems with Matrices 3. Exponential Functions (1) You can enter the growth/decay factor b in y = bx and watch the effects on the resulting graph of changing it. (2) You can enter two points and change either of them to see the effects. 4. Doubling Time & Half-Life Investigate the relationship between the growth factor b and the doubling time or the decay factor b and the half-life time of an exponential decay process.

5. Power Functions Behavior based on the power p. 6. Sum of the Squares to measure how well a line fits a set of data. 7 DataFit Fitting linear, exponential, and power functions to data. 8. The Logistic Model Investigate two different aspects of the discrete logistic model based on the logistic difference equation P n+1 = aP n - bP n 2. (1) Enter values for a and b and the initial population value P 0 and see the effects on the resulting population curve. (2) The effects of changes in the initial growth rate a and the maximum sustainable population (the limit to growth), along with the initial population value P 0. 9 Quadratic Functions Investigate: (1) Enter the three coefficients in a quadratic function and see the resulting graph. (2) Enter three points and see the effects on the graph. 10. Cubic Functions Investigate: (1) Enter the four coefficients in a cubic function and see the resulting graph. (2) Enter four points and see the effects on the graph.

11. Quartic Functions 12. Polynomials Investigate any polynomial up to eighth degree by entering the values for the coefficients. You also control a point on the graph to see the coordinates of that point and so locate real roots, turning points, and inflection points. 13. End Behavior: A Polynomial vs. Its Power Function Investigate the end behavior of any polynomial up to eighth degree. You enter the values for the coefficients. 14. Graph of a Function 15. Shifting and Stretching Investigate the four different aspects of shifting and stretching/squeezing a function using a zig-zag function (basically a saw-tooth wave that serves as a precursor to the sine function). (1) The effects of changing the parameters a and c in y - c = zig (x - a). (2) The effects of changing the parameters k and m in k * y = zig (m * x).

16. Normal Distribution Function Investigate the normal distribution function based on its two parameters: the mean µ (horizontal shifts) and the standard deviation σ (vertical stretches and squeezes). 17. Visualizing Cosine and Sine Introduce the graphs of the cosine and sine functions based on a clock’s minute hand. 18. Sinusoidal Functions Investigate the effects of the four parameters A, B, C, and D on the sinusoidal functions y = A + Bsin (C(x - D)) and y = A + Bcos (C(x - D)) as vary the the midline, the amplitude, the frequency, and the phase shift. 19. Fitting Sinusoidal Functions to Data 20. Approximating Sinusoidals Investigate approximating a sinusoidal function with a polynomial up to sixth degree in the form y = a + (1/b)x + (1/c)x2+ (1/d)x3 + (1/e)x4 + (1/f)x5 + (1/g)x6, where the parameters are all integers. The sum of the squares provides a numerical measure for the goodness of the fit.

21. Approximating the Exponential Function Investigate approximating the exponential function y = b x with a polynomial up to fifth degree. 22. Approximating the Natural Logarithmic Function All of these DIGMath Excel spreadsheets for College Algebra and Precalculus are available for downloading from the speaker’s website: farmingdale.edu\~gordonsp

11. Quartic Functions 12. Polynomials Investigate any polynomial up to eighth degree by entering the values for the coefficients. You also control a point on the graph to see the coordinates of that point and so locate real roots, turning points, and inflection points. 13. End Behavior: A Polynomial vs. Its Power Function Investigate the end behavior of any polynomial up to eighth degree. You enter the values for the coefficients. 14. Graph of a Function 15. Shifting and Stretching Investigate the four different aspects of shifting and stretching/squeezing a function using a zig-zag function (basically a saw-tooth wave that serves as a precursor to the sine function). (1) The effects of changing the parameters a and c in y - c = zig (x - a). (2) The effects of changing the parameters k and m in k * y = zig (m * x).