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.
The function f defined by the relation f(x) = −2x² + 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.