The TI-Nspire Locus tool and Geometry Trace provide two options for “seeing” an entire function given by the path of a point (x,y) as the point on the x-axis is dragged.

Here’s how to use the Locus tool to investigate this new function:

1. Press [MENU]→Construction→Locus to invoke the Locus tool.

2. Move the cursor to point (x,y) (the point whose path you're interested in viewing) and press [CLICK].

3. Move the cursor to the point on the x-axis, the driver point, and press [CLICK].

4. Press [ESC] to exit the Locus tool.

The first screen shows the result of using the Locus tool. Its attributes are changed to dashed and its thickness changed to medium to provide some contrast from the other graphed function.

Geometry Trace offers another way to see this relationship. Hover over the locus, press [CLICK][MENU]→Delete to delete the locus, and follow these steps:

1. Press [MENU]→Trace→Geometry Trace to invoke the Geometry Trace tool.

2. Move the cursor to point (x,y) (the point whose path you're interested in viewing) and press [CLICK].

3. Move the cursor to the point on the x-axis, the driver point, and press [CTRL][CLICK] to grab the point.

4. Use the Touchpad keys to move the grabbed point along the x-axis and watch the trace appear on the screen.

5. Press [ESC] to exit the Geometry Trace tool.

This is a nice way to see the graph of the derivative of a function. Using the Geometry Trace tool enables you to control how fast the derivative is formed. The quicker you drag the point on the x-axis, the fewer points are left behind in the trace track.

Incidentally, a limit of 150 points is left in the track. The older parts of the track begin to fade out as you continue to track the movement of the point.

The locus is tied to the coordinate plane. If you adjust the window settings, the locus adjusts accordingly. On the other hand, the Geometry Trace is not tied to the coordinate plane. Rather, it is as a geometric object overlaid on top of the coordinate plane. If you move or adjust the coordinate plane, the Geometry Trace does not move with it.

Press [MENU]→Trace→Erase Geometry Trace to erase the Geometry Trace.