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sometimes, we come across a function that requires more than one formula in order to obtain the given output. a piecewise function is a function in which more than one formula is used to define the output over different pieces of the domain. we use piecewise functions to describe situations in which a rule or relationship changes as the input value crosses certain “boundaries.” for example, we often encounter situations in business for which the cost per piece of a certain item is discounted once the number ordered exceeds a certain value. a piecewise function is a function in which more than one formula is used to define the output. write a function relating the number of people, [latex]n[/latex], to the cost, [latex]c[/latex].

the function is represented in figure 21. the graph is a diagonal line from [latex]n=0[/latex] to [latex]n=10[/latex] and a constant after that. a cell phone company uses the function below to determine the cost, [latex]c[/latex], in dollars for [latex]g[/latex] gigabytes of data transfer. the function is represented in figure 22. we can see where the function changes from a constant to a shifted and stretched identity at [latex]g=2[/latex]. we plot the graphs for the different formulas on a common set of axes, making sure each formula is applied on its proper domain. at the endpoints of the domain, we draw open circles to indicate where the endpoint is not included because of a less-than or greater-than inequality; we draw a closed circle where the endpoint is included because of a less-than-or-equal-to or greater-than-or-equal-to inequality.

graph piecewise-defined functions tax brackets are another real-world example of piecewise functions. below are the three components of the piecewise function graphed on separate coordinate example: when x is less than 2, it gives x ,; when x is exactly 2 it gives 6; when x is more than 2 and less than or equal , piecewise functions graphing, piecewise functions graphing, how to graph piecewise functions step by step, piecewise functions examples and answers, graphing piecewise functions worksheet.

we have seen many graphs that are expressed as single equations and are continuous over a domain of the real numbers. piecewise defined functions may be continuous (as seen in the example piecewise-defined functions can also have discontinuities (“jumps”). the function in the example below has piecewise function. create accountorsign in. y = x <−1:3−1 x +1 2. 1. y = −1< x <1:1.5+1 x +1. 2. y = 1< x <2: x −1 , piecewise function grapher, piecewise defined function graph, piecewise defined function graph, piecewise functions, domain and range, evaluating piecewise functions worksheet

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