An animation of your first example, $y=x(x−1)(x+1)$.
The animation is flawed in that it jumps jarringly when the tick labels reach the boundary. I removed the ticks and labels, which gains smoothness at the expense of
magnitude feedback. (The previous version is here.)
And I limited the number of frames so that the file would not be too huge (it is ~700KB 1MB now).
Frame rate is browser and processor dependent. At best this gives an idea of what a more
professional animation might look like.

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3 | File got larger; updated size. | ||
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2 | Spelling! | ||
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An animation of your first example, $y=x(x−1)(x+1)$.
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An animation of your first example, $y=x(x−1)(x+1)$.
The animation is flawed in that it jumps jarringly when the tic labels reach the boundary,
and I limited the number of frames so that the file would not be too huge (it is ~700KB now).
Frame rate is browser and processor dependent. At best this gives an idea of what a more
professional animation might look like.
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