![]() What is a Discontinuous Function Example?Īn example of a discontinuous function is f(x) = 3/(2x - 4) as the function is not defined at x = 2. ![]() Hence, a discontinuous function is not differentiable at the point of discontinuity. If a function is discontinuous at a point, then automatically the function becomes not differentiable at that point. Is a Discontinuous Function Differentiable? There are three types of discontinuities of a discontinuous function, namely removable, jump, and infinite discontinuities. What are the Types of Discontinuous Function? Usually, there is a point of discontinuity, but there is an asymptote in the case of essential discontinuity. An infinite discontinuity is easily visible. The value of the function cannot be evaluated at this point as the values tend towards infinity left ( infty right) (). Many functions have asymptotic curves that spike to infinite values near the asymptote. We can identify if a function is a discontinuous function using a graph if the graph has breaks, jumps, gaps, or holes. You might note one more thing in essential discontinuity. An infinite discontinuity is a result of the nature of the function under evaluation. How Do You Identify a Discontinuous Function Using a Graph? The left-hand and right-hand limits of the function at x = a exist but are not equal.The left-hand limit and right-hand limit of the function at x = a exist and are equal but are not equal to f(a).Ī function is said to be a discontinuous function if any of the following cases is satisfied:.The left-hand limit and right-hand limit of the function at x = a exist but are not equal.A discontinuous function has breaks or gaps on its graph.įAQs on Discontinuous Function What is a Discontinuous Function in Math?Ī function f is said to be a discontinuous function at a point x = a in the following cases:.The given function is polynomial, and is defined for all values of x, so we can find the limit by direct substitution: lim x 2x3 4x 23 4(2) 0. There are three types of discontinuities of a function - removable, jump and essential. Evaluate using continuity, if possible: lim x 2 x3 4x.A function that is not continuous is a discontinuous function.Important Notes on Discontinuous Function ![]() One of the two left-hand and right-hand limits can also not exist in such discontinuity. It is called 'infinite discontinuity' or 'essential discontinuity'.
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