Challenge Level

Don't be afraid to experiment and sketch lots of rough curves before neatly drawing any new examples which you construct.

A continuous curve can be a straight line, or a collection of straight line segments which join together.

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/or number of points with zero gradient, along with other conditions that you might impose.