![]() ![]() The reason is that each part of the piecewise function should have its own interval in the domain, which should not overlap with the interval of other parts. The parts of a single piecewise function do not intersect or overlap. ![]() ![]() Note that this function is not continuous at x = 1, where the left and right intervals meet. The inequality symbol at the right is inclusive, so we use a closed circle at x = 5. The inequality symbol at the left is strict, so we use an open circle at x = 1. This is a linear function, and the endpoints are x = 1 (left) and x = 5 (right). Next, we look at the function f(x) = -2x – 4. You can see the graph of this function below. Example 1: A Piecewise Function With Two PartsĬonsider the piecewise function defined by: What Is A Piecewise Function?Ī piecewise function has two or more different parts, each of which is defined by a separate function on an interval in the domain. We’ll also take a look at some examples to make the concepts clear. In this article, we’ll talk about piecewise functions and answer some common questions about them. Of course, a piecewise function can have two, three, or more different parts – the key is that each part is defined on a different interval (there is no overlap). It may also have extrema (maximum or minimum values), including at its endpoints. A piecewise function may have an inverse if it is one-to-one. A piecewise function may or may not be continuous or differentiable. So, what is a piecewise function? A piecewise function is defined by multiple functions, one for each part of a domain. They are sometimes called “hybrid functions”, which gives us a hint about their nature. Piecewise functions are often used in algebra and calculus to describe behavior that does not follow a single function for an entire interval. ![]()
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