Piecewise Defined FunctionsHow to Write a Weird FunctionAbsolute Value FunctionSlide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13AssignmentPiecewise Defined FunctionsLesson 2.3How to Write a Weird Function•What if we had to write a single function to describe this graph …•We must learn how to specify different formulas for different parts of the domainAbsolute Value Function•Whatever you put into the functioncomes out positive-3+3+7+7Absolute Value Function•Definition00)(xifxxifxxabsxUse the abs( ) function on your calculatorUse the abs( ) function on your calculatorAbsolute Value Function•Note the graph of y = | x |•Table of valuesPiecewise Defined Functions•Consider a function defined differently for different parts of the domain (the x values)•Consider what the table of values looks like 2 for x x2 x 0for 2)(2xxfPiecewise Defined Functions 2 for x x2for x 2)(2xxfx y-101234Piecewise Defined Functions•Our calculatorhandles piecewisefunctions with thewhen ( ) command 2 for x x2for x 2)(2xxfWhat will the graph look like?What will the graph look like?Use Diamond 0 for the ≤ signUse Diamond 0 for the ≤ signPiecewise Defined FunctionsPiecewise Defined Functions•Condition•Expression to usewhen conditionis true•Expression to use when condition is falsePiecewise Defined Functions•Try entering and graphing the following function2 for x 42 for x x - 4)(xgPiecewise Defined Functions•Alternative methodPiecewise Defined Functions4 - x for x 2( )4 for x 2g xx<�=�- ��Assignment•Lesson 2.3•Page 83•Exercises 1 – 14
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