Continuity and discontinuity
If considering a function we can see that there are
no "gaps" in the curve. Any value of x will give us a
corresponding value of y. We could continue the graph in the negative
and positive directions, and we would never need to take the pencil off the
paper. Such functions are called continuous functions.
In simple English:
On the one hand, the graph of a continuous function can be drawn without lifting the pencil from the paper.
On the other hand, the
graph of a discontinuous function
cannot be drawn without lifting the
pencil from the paper.
