Connects input value on one line with output value on another line. Lines can be manipulated (rotated, scaled), input can be dragged, transformation can be altered.
<begin brainstorm>
Start w/o color, lines on top of each other. hard to see what happens with every point, so colorize and turn on traces. Still hard to see what happens, because colors are overlapping, so drag output line down; now easier to see what is happening, but still not perfect -- for instance, some functions map different inputs to the same output, which results in overlapping colors again. Thought: increase the height of the colorizing segment as input moves further from the origin. This will allow colors to appear "stacked" on top of each other [note: not implemented in this sketch]. --OR-- Thought: colorize a point moving down the vector showing the transformation, position based on distance input is from origin [note: not implemented in this sketch]. --OR-- Thought: Skip the colors, use space by spinning output line perpendicular, uniquely drawing point that connects input information with output information (two options: draw point half-way between input and output with 180degree angle; draw point 90degrees from both. [thought: in general, 180 - angle[input line, output line]?]).
Use to discuss ordered pairs; domain and range...
Began as a desire to show one coordinate system (x-axis) being transformed into another (u-axis) to help understand u-substitution.
</end brainstorm>
