{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 261 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Title" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 1 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }{PSTYLE "Author" 0 19 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } 3 0 0 -1 8 8 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 21 "Exponential Functions" }} {PARA 19 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 36 "We are i nterested in the graphs of " }{XPPEDIT 18 0 "f(x) = a^x;" "6#/-%\"fG6 #%\"xG)%\"aGF'" }{TEXT -1 8 ", where " }{TEXT 256 3 "a >" }{TEXT -1 3 "1. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "Example 1: If " } {XPPEDIT 18 0 "f(x) = 2^x;" "6#/-%\"fG6#%\"xG)\"\"#F'" }{TEXT -1 7 ". \+ Then " }}{PARA 0 "" 0 "" {TEXT -1 12 "(1) plot f; " }}{PARA 0 "" 0 "" {TEXT -1 12 "(2) what is " }{TEXT 257 6 "f(0); " }}{PARA 0 "" 0 "" {TEXT -1 41 "(3) what happens to f when x gets large (" }{XPPEDIT 18 0 "infinity;" "6#%)infinityG" }{TEXT -1 4 ") ? " }}{PARA 0 "" 0 "" {TEXT -1 41 "(4) what happens to f when x gets small (" }{XPPEDIT 18 0 "-infinity;" "6#,$%)infinityG!\"\"" }{TEXT -1 2 ")?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "f:=x->2^ x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG% &arrowGF()\"\"#9$F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 " plot(f,-5..5,-1..10);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$7W7$$!\"&\"\"!$\"1++++++DJ!#<7$$!1LLLe%G?y% !#:$\"1a49K%yYj$F-7$$!1mmT&esBf%F1$\"1'>c+P?`9%F-7$$!1LL$3s%3zVF1$\"1A qguGy0[F-7$$!1ML$e/$QkTF1$\"1')RNew$pd&F-7$$!1nmT5=q]RF1$\"1rqQf*esY'F -7$$!1LL3_>f_PF1$\"1*GFd6.#>uF-7$$!1++vo1YZNF1$\"1\"RoHR#z_&)F-7$$!1LL 3-OJNLF1$\"1)*[NCyk2**F-7$$!1++v$*o%Q7$F1$\"1zU?!frr9\"!#;7$$!1mmm\"RF j!HF1$\"1k<\"f%R&QL\"Ffn7$$!1LL$e4OZr#F1$\"1$))G8X\"HB:Ffn7$$!1+++v'\\ !*\\#F1$\"1-yM\"zJ*o$[Ffn7$$!1$***\\(=[jL)Ffn$\"1WIZQv 86cFfn7$$!1'***\\iXg#G'Ffn$\"18Y1)=g&pkFfn7$$!1emmT&Q(RTFfn$\"1!G;%3:` 0vFfn7$$!1lm;/'=><#Ffn$\"1\\on?AQ-')Ffn7$$!1EMLLe*e$\\!#=$\"1CP0Pa%e'* *Ffn7$$\"1sm;zRQb@Ffn$\"1V,:dr8h6F17$$\"1-+](=>Y2%Ffn$\"1e95g.NE8F17$$ \"1vmm\"zXu9'Ffn$\"1;!*enoGJ:F17$$\"1,+++&y))G)Ffn$\"1)=X=]:jx\"F17$$ \"1++]i_QQ5F1$\"1\")*Qk]FR0#F17$$\"1,+D\"y%3T7F1$\"1=;N)*>wjBF17$$\"1+ +]P![hY\"F1$\"1;(z3QKGw#F17$$\"1LLL$Qx$o;F1$\"1yWo[*o&yJF17$$\"1+++v.I %)=F1$\"1,PkD&QFcx7$$\"1ommmx GpVF1$\"166uhRum?Fcx7$$\"1M$eRA5\\Z%F1$\"1Z75p2tBAFcx7$$\"1++D\"oK0e%F 1$\"1dNhh?k#R#Fcx7$$\"1,++]oi\"o%F1$\"1#>VV(eJmDFcx7$$\"1,+v=5s#y%F1$ \"1/l.$3'f_FFcx7$$\"1,]P40O\"*[F1$\"1o=f(Gzy'HFcx7$$\"\"&F*$\"#KF*-%'C OLOURG6&%$RGBG$\"#5!\"\"F*F*-%+AXESLABELSG6$%!GFj\\l-%%VIEWG6$;F(F\\\\ l;$Ff\\lF*$Fe\\lF*" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "f (100);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"@w`?.n\\,%H#G-g]wE\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "evalf(f(-100));" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+_!4'))y!#S" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 258 77 "Exercise 1: Answer the qu estions listed in \"Example 1\" by using the function " }{XPPEDIT 18 0 "f(x) = 10^x;" "6#/-%\"fG6#%\"xG)\"#5F'" }{TEXT -1 1 "." }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 109 "Example 2: Use th e shifting/reflection techniques to graph the each of the following fu nctions together with " }{XPPEDIT 18 0 "f(x) = 2^x;" "6#/-%\"fG6#%\"xG )\"\"#F'" }{TEXT -1 61 ".[Do them by hands first and verify your answe rs with Maple]." }}{PARA 0 "" 0 "" {TEXT -1 4 "(1) " }{XPPEDIT 18 0 "f 1(x) = 2^x+2;" "6#/-%#f1G6#%\"xG,&)\"\"#F'\"\"\"F*F+" }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 4 "(2) " }{XPPEDIT 18 0 "f2(x) = 2^x-2;" "6 #/-%#f2G6#%\"xG,&)\"\"#F'\"\"\"F*!\"\"" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "(3) " }{XPPEDIT 18 0 "f3(x) = 2^(x-2);" "6#/-%#f3G6#%\" xG)\"\"#,&F'\"\"\"F)!\"\"" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "(4) " }{XPPEDIT 18 0 "f4(x) = 2^(x+2);" "6#/-%#f4G6#%\"xG)\"\"#,&F' \"\"\"F)F+" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "(5) " } {XPPEDIT 18 0 "f5(x) = 2^(-x);" "6#/-%#f5G6#%\"xG)\"\"#,$F'!\"\"" } {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 4 "(6) " }{XPPEDIT 18 0 "f6(x ) = -2^x;" "6#/-%#f6G6#%\"xG,$)\"\"#F'!\"\"" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "f1: =x->2^x+2;f2:=x->2^x-2;f3:=x->2^(x-2);f4:=x->2^(x+2);f5:=x->2^(-x);f6: =x->-2^x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f1Gf*6#%\"xG6\"6$%)ope ratorG%&arrowGF(,&)\"\"#9$\"\"\"F.F0F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f2Gf*6#%\"xG6\"6$%)operatorG%&arrowGF(,&)\"\"#9$\"\" \"!\"#F0F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f3Gf*6#%\"xG6\"6$ %)operatorG%&arrowGF()\"\"#,&9$\"\"\"!\"#F0F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f4Gf*6#%\"xG6\"6$%)operatorG%&arrowGF()\"\"#,&9$\"\" \"F-F0F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f5Gf*6#%\"xG6\"6$%) operatorG%&arrowGF()\"\"#,$9$!\"\"F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f6Gf*6#%\"xG6\"6$%)operatorG%&arrowGF(,$)\"\"#9$!\"\"F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 259 5 "Note." }{TEXT -1 166 " The foll owing Maple syntax is to plot two functions together. 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Given that " }{XPPEDIT 18 0 "f(x) \+ = 3^x+2;" "6#/-%\"fG6#%\"xG,&)\"\"$F'\"\"\"\"\"#F+" }{TEXT -1 1 "." }} {PARA 0 "" 0 "" {TEXT -1 10 "(a) Find " }{TEXT 260 1 "g" }{TEXT -1 65 " that is being horizontally shifted to the right 3 units from f. " }}{PARA 0 "" 0 "" {TEXT -1 10 "(b) Find " }{TEXT 261 1 "h" }{TEXT -1 56 " that is being vertically shifted down 5 units from g." }} {PARA 0 "" 0 "" {TEXT -1 84 "Note: You should be able to do this by ha nd first and verify your answer with Maple." }}{PARA 0 "" 0 "" {TEXT 263 10 "Exercise 4" }{TEXT -1 14 ": Given that " }{XPPEDIT 18 0 "f(x) = 3^(-x)+4;" "6#/-%\"fG6#%\"xG,&)\"\"$,$F'!\"\"\"\"\"\"\"%F-" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 76 "(a) Find g that is being ho rizontally shifted to the right 3 units from f." }}{PARA 0 "" 0 "" {TEXT -1 66 "(b) Find h that is being vertically shifted down 5 unit s from g." }}{PARA 0 "" 0 "" {TEXT -1 84 "Note: You should be able to \+ do this by hand first and verify your answer with Maple." }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}}}{MARK "11" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }