dicontinuity can result of non definition: examples: 3/(x-5) discontinue for x = 5 ; √(x²-4) discontinue for -2 < x < 2 limits are different to right an left of x0 example y = (x-1)²/|x-1|

A discontinuity in a function is a point where the value of the function takes a sudden jump. When a function has one, then the value that the function is heading for at that point depends on which direction you come at it from. Think of a place on the seashore where a sheer cliff overlooks the water, and the waves lap at the bottom of the cliff. The elevation is discontinuous there. If you come at it from the water, you expect the elevation to be at sea level when you get there. If you come at it from the land side, then you expect the elevation to be 100 feet there. When you actually get there, you find that the elevation takes a sudden jump there, and right at that point it's BOTH zero and 100-ft. That's a discontinuity.