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This 5 page Class Notes was uploaded by Aileen Davis on Tuesday October 20, 2015. The Class Notes belongs to MATH0012 at Sierra College taught by RebeccaKyler in Fall. Since its upload, it has received 28 views. For similar materials see /class/225372/math0012-sierra-college in Mathematics (M) at Sierra College.
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Date Created: 10/20/15
Math 12 25 Library of Functions Linear Functions mx 1 Ex Write a linear function given 1 and 5 Information from a Graph 4y Domain 3 2 Range 1 Intervals of the function increasing 5 74 73 72 71 1 2 3 4 5 Intervals of the function decreasing Intervals where the function is constant Intercepts Evaluate f 2 f 5 Piecewise Defined Functions A function where different rules are used for assigning output values on different parts of the domain 2x 2 ifxlt 1 EX fx x 2 if lelt5 3 ifoS Evaluate a f 7 b f 1 c f0 d f5 2x 2 ifxlt 1 y SkeTch fx x 2 z39f lelt5 3 ifoS STaTe The Domain STaTe The Range InTervals of Increasing InTervals of Decreasing InTervals of ConsTanT RelaTive Maximum Values and RelaTive Minimum Values The x coordinaTe of a poinT ThaT is higher lower Than any nearby poinT of a graph is called a relaTive maximum relaTive minimum value of The funcTion Even and Odd FuncTions Even FuncTion Odd FuncTion w a w w a xry yhaxis symmeTry origin symmeTry To algebraically deTermine if a funcTion is even or odd we perform The following TesTs If f x fx Then The funcTion is an even funcTion If f x Then The funcTion is an odd funcTion Examples Algebraically deTermine if a funcTion is even odd or neiTher EX1 fxx45 EXZ fxx2x 2 EX3 gx 2 5 x EvaluaTing FuncTions Given 3x 7 Find each of The following a f2x b 3 fx c d 1 Look aT The Basic FuncTions on pg 257 258 Also see The link on The class websiTe You should be able To produce These graphs yourself by ploTTing poinTs and using symmeTries You should be able To find The domain range inTervals of increasing decreasing or consTanT and wheTher The funcTion is even or odd and whaT kind of symmeTry is associaTed wiTh ThaT SecTion 3 2 1 2 A IO mh for Graphing Polynomial FuncTions Describe The farend behavior of Find The zeros of Think abouT The mulTipIiciTy and whaT ThaT means aT each X inTe rcepT Use The zeros off and TesT numbers To find The inTervals over which The graph of fis above or below The Xaxis Find The yinTercepT Find any symmeTries of The graph of The funcTion DeTermine The maximum number of Turning poinTs Graph The funcTion PloT The inTercest and The poinTs found in STep 2 any oTher poinTs ThaT you need To make a good skeTch Then noTe The farend behavior and finally skeTch a smooTh curve ThaT passes Thru a poinTs IT is imporTanT To use an appropriaTe scale on your axes DeTermining your poinTs before you sTarT skeTching will help you make ThaT decision EX Use The guidelines above To skeTch The polynomial Px x4 5x2 36 Ex Use The guidelines To skeTch The polynomial Px x2 x2 4x 2 Ex Use The guidelines To skeTch The polynomial Px 2x4 2x3 8x 16