Piecewise Functions - ClassZone

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Page 1 of 2114Chapter 2Linear Equations and FunctionsPiecewise FunctionsREPRESENTINGPIECEWISEFUNCTIONSU p to now in this chapter a function has been represented by a single equation. Inmany real-life problems, however, Functions are represented by a combination ofequations, each corresponding to a part of the domain. Such Functions are calledFor example, the Piecewise function given by (x) = is defined by two equations. One equation gives the values of (x) when xis less thanor equal to 1, and the other equation gives the values of (x) when xis greater than a Piecewise FunctionEvaluate (x) when (a) x= 0, (b) x= 2, and (c) x= 4. (x) = SOLUTIONa. (x) = x+ 2Because 0 <2, use first equation. (0) = 0+ 2 = 2Substitute 0 for (x) = 2x+ 1 Because 2 2, use second equation. (2) = 2(2) + 1 = 5Substitute 2 for (x) = 2x+ 1 Because 4 2, use second equation. (4) = 2(4) + 1 = 9Substitute 4 for a Piecewise FunctionGraph this function: (x) =SOLUTIONTo the left of x= 1, the graph is given by y= 12 x+ 23.

Page 1 of 2 2.7 Piecewise Functions 115 Graphing a Step Function Graph this function: ƒ(x) = SOLUTION The graph of the function is composed of four line segments. For instance, the first

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