![]() ![]() For example, f(x) = |x| is continuous everywhere. Which Function is Always Continuous?įor a function to be always continuous, there should not be any breaks throughout its graph. Hence, the square root function is continuous over its domain. The graph of a square root function is a smooth curve without any breaks, holes, or asymptotes throughout its domain. For example, \(g(x)=\left\\right.\) Describe the Continuity of Square Root Function. What is Piecewise Continuous Function?Ī continuous function is said to be a piecewise continuous function if it is defined differently in different intervals. The polynomial functions, exponential functions, graphs of sin x and cos x are examples of a continuous function over the set of all real numbers. The graph of a continuous function should not have any breaks. Mathematically, f(x) is said to be continuous at x = a if and only if limₓ → ₐ f(x) = f(a). Here are some topics that you may be interested in while studying continuous functions.įAQs on Continuous Function What is the Definition of Continuous Function?Ī continuous function is a function whose graph is not broken anywhere.
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