USING GSP-4 AS A DYNAMIC FUNCTION PLOTTER
We are going to use the Geometer's Sketchpad-4 to graph functions in a way that allows us to change parameters. A parameter means a value that may have different values, but doesn't vary once it is set. For example, in the linear function y = mx + b , m and b are parameters, while x and y are variables.
- Open a new sketch. Go to Edit >> Preferences >> Text >> As Objects Are Measured; set the Distance units to inches.
- To create a parameter "slider":
- Use the line tool to create a horizontal (or vertical) line AB. Use the point tool to place a point C on the line between A and B.
- Deselect all, then select, in order, points A, B and C (selecting the in-between point last. Use Measure >> Ratio to show a value for (AC/AB).
- Hide the line and point B. Construct segment AC.
- Use the Text tool to rename the ratio "AC/AB" as a parameter "M". Also, rename point A as "0" and point B as the "Drag" point.
What happens as you slide the "Drag" point closer or further away from A?
How can you get a negative value for M?
- Go to Graph >> Grid Form >> Square Grid. Notice that one point appears at the origin and another point appears at the unit value (that is, at 1) on the x-axis.
- Using the Select tool, explore what happens when you click-&-drag the origin or the unit point.
Change the grid type using Graph >> Grid Form >> Rectangular Grid. How many points show up on the grid? What happens as you move each of them?
- Now let's create the basic function y = mx. Use Graph >> Plot New Function to bring up a function "calculator". Make sure that the Function >> y=f(x) is showing. This means that GSP is set up to get the right-hand side of the equation.
Click once on the measure of M, which should make an "M" appear in the calculator screen. Click the key for multiply ("*"), then the key for "x"; click "OK".
- The expression "f(x) = Mx" should appear on-screen, and a line should appear on the grid. Move the drag point on the slider and describe what happens.
- If you want to edit a function's equation, simply double-clicking on the function will take you to the function editor.
- How would you add the parameter B to make this a model for studying a general linear equation of the form y = Mx + B?
Adding a third parameter would allow you to explore such functions as
y = Ax2 + Bx + C, or y = A(x - H)2 + K.
- The calculator has a number of built-in functions, available under Graph >> Plot New Functions >> Functions, including the three basic trig functions.
How could you illustrate the effects of the parameters A, B and C in the general trig function y = Asin(Bx) + C ? When you include a trig function, you may be prompted to think about changing the angle units from degrees to radians.