A function whose curve does not have any breaks. Its graph can be drawn without lifting the pencil from the paper.

Just as a continuous function on an interval [

*a*,*b*] must be defined for every element of the interval, its image should also not have any discontinuities.### Examples

The function *f* defined by the relation *f*(*x*) = −2*x*² + 4 on the interval [-1, 1] is a continuous function.

The step function *f* defined by the relation *f*(*x*) = 0.5 [*x* – 3] + 2 on the interval [-1, 5] is not a continuous function on the interval.