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'Curvy Catalogue' printed from http://nrich.maths.org/
Don't be afraid to experiment and sketch lots of rough curves
before neatly drawing any new examples which you construct.
Some curves get closer and closer to the $x$-axis for large values
of $x$, whereas othes get larger and larger as $x$ grows.
You could classify your curves according to the number of zeros and
turning points, along with other conditions that you might