A function is said to be continuous if its graph can be drawn without lifting the pencil. Otherwise, the function is said to be discontinuous.
A discontinuous function can have holes, jumps, or asymptotes throughout its graph.
A point where a function is discontinuous is called a discontinuity. Function I has a point of discontinuity at x=1, Function II has a point of discontinuity at x=2, and Function III has a point of discontinuity at x=0.