Could we 'see' behavior of functions using color as the second dimension? Here, a few functions are plotted and the brightness or darkness of a corresponding horizontal position depends upon the function's output. Below, an entire family of functions.

The image below shows five functions, each a larger multiple of the next (starting at the bottom). Go to the jump to reveal which function.

2014-07-25_second_dimensional_color.ggb |

The above image plots five functions: on the bottom is f(x) = x*sin(x), and the one on top is f(x) = 5x*sin(x). Below, you can play with any functions you like!