![]() I have seen a couple of other examples of questions like this online, but the domains of each piecewise function were the same. The example below will contain linear, quadratic and constant "pieces". Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Due to this diversity, there is no " parent function" for piecewise defined functions. Their "pieces" may be all linear, or a combination of functional forms (such as constant, linear, quadratic, cubic, square root, cube root, exponential, etc.). ![]() Piecewise defined functions can take on a variety of forms. Similar to a piecewise functions, we have different rules for different parts of our lives, such as before and after learning to drive. ![]() Because these graphs tend to look like "pieces" glued together to form a graph, they are referred to as " piecewise" functions ( piecewise defined functions), or " split-definition" functions.Ī piecewise defined function is a function defined by at least two equations ("pieces"), each of which applies to a different part of the domain. Piecewise Functions (Values and Graphs) Piecewise functions occur when different parts of the domain are governed by different rules, or sub-functions. Of course, a piecewise function can have two. 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. These graphs may be continuous, or they may contain "breaks". What is piecewise continuous function example A piecewise continuous function is a function that can be written as sum of two or more functions. A piecewise function is defined by multiple functions, one for each part of a domain. There are also graphs that are defined by "different equations" over different sections of the graphs. We have also seen the " discrete" functions which are comprised of separate unconnected "points". We have seen many graphs that are expressed as single equations and are continuous over a domain of the Real numbers. Piecewise Functions A Function Can be in Pieces We can create functions that behave differently based on the input (x) value. ![]()
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