A piecewise function is continuous on a given interval in its domain if the following conditions are met: its constituent functions are continuous on the corresponding intervals (subdomains), there is no discontinuity at each endpoint of the subdomains within that interval.

Is Sinx piecewise continuous?

So, |sin(x)| is continuous (therefore, piecewise continuous) but it is not differentiable (though it is piecewise smooth*) on, say, [-pi, pi]. * smooth meaning: infinitely often differentiable. d_leet said: The derivative is not continuous at 0, from the right it approaches 1, from the left it approaches -1.

Why are piecewise functions discontinuous?

A piecewise function is a function defined by different functions for each part of the range of the entire function. A discontinuous function is a function that has a discontinuity at one or more values mainly because of the denominator of a function is being zero at that points.