In this tutorial we'll look at how to plot a function and then draw a secant which we'll use to approximate a tangent to a point.
First of all we need a function, I am going to use
To enter a function, go to Graph -> Plot New Function
Type in the function you want into the window that pops up. Use the x and the ^ keys on the screen for variables and exponents. There's also options for different types of equations and functions on the drop down menus given. When you hit OK, you'll get a grid on your screen with the graph plotted.
In order to create a secant on this function we need to create two points. To do this, select the curve and go to Construct -> Point on Function Plot. Deselect everything and do this again so you'll have two points as below.
Select the two points and go to Construct -> Line
We're essentially done at this point. The two points are free to move on the function however you want and the line will always follow the points. The last thing we'll do is have GSP calculate the coordinates of the points and the slope of the line.
Select the points individually and go to Measure -> Coordinates for each. They'll also get a letter name label.
Now select the line and go to Measure -> Slope.
By repositioning the points we can approximate the slope of the tangent:
All done, want to try another?