A continuous attribute is a function whose graph is a single curve that is unbroken. Therefore, a discontinuous function is a function which is not continuous. When it has a derivative, a function is distinguishable. As the slope, you should think of a derivative of a function.
A continuous function is a function in mathematics that does not have any sudden value shifts, known as discontinuities. If not constant, it’s said that a function is discontinuous. The continuity of a function is the characteristic of a function in which a continuous wave is the graphical form of that function.