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 $x=0.$