FthmFDockDFHAMaccdDCDcCncdCCdsCCaxcrFnTb^FnIOPalatinoTxEnFnIOArialTxEnFnIODidotTxEnTblCKCmpDCmp TblC Case Table 1KCntDsCnTbCnCmRf"CTmdTablSTbHlTbGm4TGhtdbl runl@K@c@4CTsl#AtRfnAtRfx@4@DCDNdCDclCDFlCDNdCDclCDSrCmRf"DColKCmpDCmp DCol Collection 1KCntDsCngClCnCmRf"InSt7CoIn @a@b@z @xPCmPnCmPn InPmCsPnInPminTMaaTMTabl_TbHlTbGm@TGhtdbl runl@R@N@a@4Tabl_TbHlTbGm@TGhtdbl runl@R@N@a@4CtPnInPm inTMDsPnInPminTMaaTMTabl_TbHlTbGm@TGhtdbl runl@R@N@a@4Tabl_TbHlTbGm@TGhtdbl runl@R@N@a@4MsPnInPminTMaaTMTabl_TbHlTbGm@TGhtdbl runl@R@N@a@4Tabl_TbHlTbGm@TGhtdbl runl@R@N@a@4?UUUUUUCDNdCDScCollIterateCDNdCDScCDHl|ClCs AtLsrCCsAAttrCsAtCCsAxPrLsSPrLif[id[greaterthan[string[(**)"n"],num[1,"1"]]],plus[times[string[(**)"m"],customfxn"prev"[id[string[(**)"x"]]]],string[(**)"b"]],string[(**)"x1"]]CCsAAttrCsAtCCsAnPrLsSPrLstring[(**)"caseIndex"]CCmAAttr CmAtCCmADisplay PrLsSPrLAtLsCCmAAttrCmAtzCCmAOriginPrLsSPrLAtLsnCCsAAttrCsAtCCsAxPrLsSPrLCCsAAttrCsAtCCsAyPrLsSPrLCCmAAttr CmAt&CCmAPicturePrLsSPrLAtLsCCsAAttrCsAtCCsAimagePrLsSPrLCCsAAttrCsAtCCsAxPrLsSPrLCCsAAttrCsAtCCsAyPrLsSPrLCCsAAttrCsAtCCsAwidthPrLsSPrLCCsAAttrCsAtCCsAheightPrLsSPrLCCmAAttr!CmAtCCmA_CaptionPrLsSPrLAtLsCCsAAttr CsAtCCsAcaptionPrLsSPrLCCsAAttrCsAtCCsAxPrLsSPrLCCsAAttrCsAtCCsAyPrLsSPrLCDNdCDScCDHl XHmCAAtLs NHCAtAttrCsAtHCAtxPrLsSPrLFrCAHmCDFrCAif[id[greaterthan[string[(**)"n"],num[1,"1"]]],plus[times[string[(**)"m"],customfxn"prev"[id[string[(**)"x"]]]],string[(**)"b"]],string[(**)"x1"]]HCAtAttrCsAtHCAt<nPrLsSPrLFrCAHmCDFrCA(string[(**)"caseIndex"]SApCAttr CmAt FxCAGmCmAppCSApCDisplay PrLsSPrLAtLs OrGeAttrCmAtOrGeOriginPrLsSPrLAtLsHCAtAttrCsAtHCAtxPrLsSPrLRelCHmCDNCsDRelC@@@V@b@i@p@@@V@b@i@p@@@V@b@i@p@@@V@b@i@pHCAtAttrCsAtHCAtyPrLsSPrLRelCHmCDNCsDRelC@8@8@8@8@8@Q@Q@Q@Q@Q@\@\@\@\@\@c@c@c@c@cIcGeAttr CmAtFxCAGmCmIcGePicturePrLsSPrLAtLsHCAtAttrCsAtHCAtimagePrLsSPrLGnCAHmCDGnCA````````````````````HCAtAttrCsAtHCAtxPrLsSPrLRelCHmCDNCsDRelCHCAtAttrCsAtHCAtyPrLsSPrLRelCHmCDNCsDRelCHCAtAttrCsAtHCAtwidthPrLsSPrLRelCHmCDNCsDRelC@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0HCAtAttrCsAtHCAtheightPrLsSPrLRelCHmCDNCsDRelC@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0@0CpGeAttr!CmAtFxCAGmCmCpGe"_CaptionPrLsSPrLAtLsHCAtAttr CsAtHCAtcaptionPrLsSPrLStrCHmCDStrCa casea casea casea casea casea casea casea casea casea casea casea casea casea casea casea casea casea casea casea caseHCAtAttrCsAtHCAtxPrLsSPrLRelCHmCDNCsDRelCHCAtAttrCsAtHCAtyPrLsSPrLRelCHmCDNCsDRelC@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ Arial@& ClOrThngCmThAtLsThngAttr ThngPComment PrLsSPrL LPart of a series on iteration, by Henri Picciotto www.picciotto.org/math-edCtSLCDNdCDclCDFlDCOrClOrDCOrAbIM$INMd.@a@b@z @xP@a@b@z @xP?UUUUUUgrafKCmpDCmpgrafGraph 1KCntDsCn&GrCnCmRf"InStCsInObIn@h@\@}@vObPnCsPnInPminTMaaTMTabl_TbHlTbGm@TGhtdbl runl@R@N@a@4Tabl_TbHlTbGm@TGhtdbl runl@R@N@a@4ObPnInPminTMaaTMTablS TbHlTbGm4TGhtdbl runl@R@i @4TablSTbHlTbGm4TGhtdbl runl@R@i@4CDNdCDclCDFlGrafATpl6AtRfnAtRfxAxlsaxclAXISaxcdaxcl0n?@5@@5axclAXISaxcdaxcl0x?@@@@@annmanenannmannmanenannmannmanenannmannmanenannmpllsPtopMLPlPcseplsc*pllsanbvanenanbv?CmRf"GrLyGrafATpl6AtRfnAtRfxAxlsaxclAXISaxcdaxcl0n?@5@@5axclAXISaxcdaxcl0x?@@@@@annmanenannmannmanenannmannmanenannmannmanenannmpllsPtopMLPlPcseplsc*pllsanbvanenanbv?annmanenannmannmanenannmannmanenannmannmanenannmGrSp"OperNVnc pointSize@CDNdCDclCDSAslidKCmpDCmp slidSlider 1KCntDsCnJSlCnCmRf"InSt!CsInObIn@ @@(@hObPnInPminTMaaTMTabl_TbHlTbGm@TGhtdbl runl@R@N@a@4Tabl_TbHlTbGm@TGhtdbl runl@R@N@a@4SlMdOperGlVlNVncm?噙m?噙AXISaxcdaxcl0????OperNVncMax_updates_per_secondslidKCmpDCmp slidSlider 2KCntDsCnJSlCnCmRf"InSt!CsInObIn@@v@L@ObPnInPminTMaaTMTabl_TbHlTbGm@TGhtdbl runl@R@N@a@4Tabl_TbHlTbGm@TGhtdbl runl@R@N@a@4SlMdOperGlVlNVncb@b@AXISaxcdaxcl0?@@@OperNVncMax_updates_per_secondslidKCmpDCmp slidSlider 3KCntDsCnJSlCnCmRf"InSt!CsInObIn@j@H@~@ObPnInPminTMaaTMTabl_TbHlTbGm@TGhtdbl runl@R@N@a@4Tabl_TbHlTbGm@TGhtdbl runl@R@N@a@4SlMdOperGlVlNVncx1@7x1@7AXISaxcdaxcl0?@@@@@?OperNVncMax_updates_per_second textKCmptextKCntTxCn This file is to explore the iteration of the function y=mx+b. The attribute n is simply there to make it easier to refer to the caseIndex. The formula says that if n is greater than 1, the current value of x is calculated by substituting its previous value into the formula mx+b. Otherwise (for the first value of x) use x1. How are the orbits affected by the values of x1, m, and b? Animate the sliders and try to understand what happens. For a given m, and b, is there a value of x1 for which the whole orbit remains constant? Such a value is called a fixed point. Use algebra to find the fixed point for given values of m and b. Use algebra to find a formula for the fixed point in terms of m and b. Graph it by using "Plot Function" in the Graph menu. For what values of m and b is there no fixed point? For what values of m and b is there an attracting fixed point? For what values is it repelling?<>>>>>><0>>>>>>>><0>>>>>>>>>>>>>>>>>>>>>>>>>>>>><0>>>>>>>>>>>>>>><0>>><0>>>>>>>>>>>>>>>>>>><0>>>>>>><0>>>>>>>>>><0>>>>>>>>><0>>>>>>>>>>>>>>>>>>>>>>>MfsS  textKCmptextKCntTxCnWFind work sheets on iterating linear functions at www.picciotto.org/math-ed/iterating<0>>>MfsS  SFmsJCTbFCmpFNdspFFltFCTbF@q0@fram@$@TCmRf"ColFCmpFNdspFFltFColF@C@Gfram@$@4CmRf"SldFCmpFNOffFSldF@|p@Rfram@@@qCmRf"GrpFCmpFNdspFFltFGrpF@~@ofram@@@.CmRf"TxtFCmpFNTxtF@h`@fram@r@KCmRf" SldFCmpFNOffFSldF@j@@Rfram@h@wpCmRf"SldFCmpFNOffFSldF@j@@Rfram@h@~PCmRf"TxtFCmpFNTxtF@j@Qfram@@@CmRf" B