{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 Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 0 1 0 128 0 1 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 128 0 1 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 128 128 1 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 128 128 128 1 0 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 1 0 1 0 2 2 0 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Cour ier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Error" -1 8 1 {CSTYLE "" -1 -1 "Courier" 1 10 255 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output " -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 } 3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE " " -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {PARA 0 "" 0 "" {TEXT 257 49 "High School Modules > Algebra by Gregory A. Moore" }}{PARA 3 "" 0 "" {TEXT -1 4 " " }{TEXT 256 21 " Functions & Relations" }}{PARA 0 "" 0 "" {TEXT -1 128 "\nThe definitio n of a function, and the connection with relations, domains and ranges , numeric and algebraic views of functions.\n" }}{PARA 0 "" 0 "" {TEXT 258 153 "[Directions : Execute the Code Resource section first. \+ Although there will be no output immediately, these definitions are us ed later in this worksheet.]" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 7 "0. Code" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "restart; with(plots): " }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 161 "Domain := proc( SET )\n local \+ domain, k;\n domain := \{\};\n for k from 1 to nops(SET) do\n \+ domain := domain union \{SET[k][1]\};\n od:\n domain;\nend proc:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 160 "Range := proc( SET )\n local range, k;\n range := \{\};\n for k from 1 to nops(SET) do \n range := range union \{SET[k][2]\};\n od:\n range;\nend pro c: \n " }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 30 "1. Relations, Domai ns & Ranges" }}{PARA 0 "" 0 "" {TEXT -1 150 "\nA relation is any pairi ng of values. A function is a special type of relation where each of t he first type of item only has one of the second type. \n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 122 "fruity_colors := \{ [apple,red],[b anana,yellow],[kiwi,green],\n [cherry,red],[lemon,ye llow],[pear,green]\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%.fruity_col orsG<(7$%&appleG%$redG7$%'bananaG%'yellowG7$%%kiwiG%&greenG7$%'cherryG F(7$%&lemonGF+7$%%pearGF." }}}{PARA 0 "" 0 "" {TEXT -1 186 "\nThe firs t element of each pair is a fruit, and the second element is the color of the fruit. The set of all fruits is the domain of the relation, an d the set of all colors is the range." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "Domain(fruity_colors);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<(%&appleG%'bananaG%%kiwiG%'cherryG%&lemonG%%pearG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "Range(fruity_colors);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#<%%$redG%'yellowG%&greenG" }}}{PARA 0 "" 0 "" {TEXT -1 34 "\nLets look at some other examples." }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 213 "Baseball_teams := \{ [Los_Angeles, Dodgers], \+ [New_York, Yankees], \n [Toronto, Blue_Jays], [San_F rancisco,Giants],\n [Atlanta,Braves] \};\n`domain `= Domain(%);\n`range ` = Range(%%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%/Baseball_teamsG<'7$%,Los_AngelesG%(DodgersG7$%)New_YorkG%(YankeesG7 $%(TorontoG%*Blue_JaysG7$%.San_FranciscoG%'GiantsG7$%(AtlantaG%'Braves G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%(domain~G<'%,Los_AngelesG%.San_ FranciscoG%)New_YorkG%(TorontoG%(AtlantaG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%'range~G<'%*Blue_JaysG%(DodgersG%(YankeesG%'GiantsG%' BravesG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 218 "Typcal_foods := \{ [America, hotdog], [Mexico, Taco], \n [Japan, Su shi], [India,Naan],[Middle_East,felafel],\n [Vietnam ,Pho] \};\n`\\n the domain `= Domain(%);\n`\\n the range ` = Range(%%) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%-Typcal_foodsG<(7$%(AmericaG%'h otdogG7$%'MexicoG%%TacoG7$%&JapanG%&SushiG7$%&IndiaG%%NaanG7$%,Middle_ EastG%(felafelG7$%(VietnamG%$PhoG" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/ %.|+~the~domain~G<(%,Middle_EastG%(AmericaG%'MexicoG%&JapanG%&IndiaG%( VietnamG" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/%-|+~the~range~G<(%'hotdo gG%%TacoG%&SushiG%%NaanG%$PhoG%(felafelG" }}}{PARA 0 "" 0 "" {TEXT -1 49 "\nWe can also have relations of numbers of course." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 100 "Number_set := \{ seq([k, k^2], k = 1..9) \};\n`\\n the domain `= Domain(%);\n`\\n the range ` = Range(%% );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+Number_setG<+7$\"\"\"F'7$\"\" #\"\"%7$\"\"$\"\"*7$F*\"#;7$\"\"&\"#D7$\"\"'\"#O7$\"\"(\"#\\7$\"\")\"# k7$F-\"#\")" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/%.|+~the~domain~G<+\" \"\"\"\"#\"\"$\"\"%\"\"&\"\"'\"\"(\"\")\"\"*" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/%-|+~the~range~G<+\"\"\"\"\"%\"\"*\"#;\"#D\"#O\"#\\\"# k\"#\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 110 "Number_set := \+ \{ seq([(k-2)^2, (k-4)^2], k = 1..7) \};\n`\\n the domain `= Domain(%) ;\n`\\n the range ` = Range(%%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% +Number_setG<)7$\"\"\"F'7$F'\"\"*7$\"\"!\"\"%7$F,F+7$F)F'7$\"#;F,7$\"# DF)" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/%.|+~the~domain~G<(\"\"!\"\"\" \"\"%\"\"*\"#;\"#D" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/%-|+~the~range~ G<&\"\"!\"\"\"\"\"%\"\"*" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 24 "2. \+ Functions & Relations" }}{PARA 0 "" 0 "" {TEXT -1 289 "\nA relation is any pairing of values. A function is a special type of relation where each of the first type of item only has one of the second type. The s et of fruity colors is function because each fruit has only one color \+ - even though some fruit may have the same color as other fruit.\n" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 142 "fruity_colors := \{ [apple, red],[banana,yellow],\n [cherry,red],[lemon,yellow] \};\n`\\ndomain`= Domain(%);\n`\\nrange` = Range(%%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%.fruity_colorsG<&7$%&appleG%$redG7$%'bananaG%'ye llowG7$%'cherryGF(7$%&lemonGF+" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/%(| +domainG<&%&appleG%'bananaG%'cherryG%&lemonG" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/%'|+rangeG<$%$redG%'yellowG" }}}{PARA 0 "" 0 "" {TEXT -1 120 "\nIn this next case, some of the values of the domain have mor e than one value of the range. Thus this is NOT a function." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 294 "country_and_cities := \{ [Canada, \+ Toronto], [Canada, Montreal], [USA, New_York],\n [ USA, Los_An geles], [Mexico, Guadalajara], [Japan, Osaka],\n [ Japan, Toky o], [Russia, Moscow], [India, Bombay], \n [India, Delhi]\};\n` \\n the domain `= Domain(%);\n`\\n the range ` = Range(%%);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%3country_and_citiesG<,7$%'CanadaG%(Toronto G7$F'%)MontrealG7$%$USAG%)New_YorkG7$F,%,Los_AngelesG7$%'MexicoG%,Guad alajaraG7$%&JapanG%&OsakaG7$F4%&TokyoG7$%'RussiaG%'MoscowG7$%&IndiaG%' BombayG7$F<%&DelhiG" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/%.|+~the~domai n~G<(%'MexicoG%&JapanG%&IndiaG%$USAG%'CanadaG%'RussiaG" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/%-|+~the~range~G<,%,Los_AngelesG%)New_YorkG%)Mont realG%,GuadalajaraG%(TorontoG%&OsakaG%&TokyoG%'MoscowG%'BombayG%&Delhi G" }}}{PARA 0 "" 0 "" {TEXT -1 310 "\nLook closely at these number set s. In the first set, each x value has only one y value. But this is no t true in the second example. A function is a relation for which each \+ member of the domain only is only associated with one member of the ra nge. Thus the first set is a function, while the second one is not." } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 100 "Number_set := \{ seq([k, k ^2], k = 1..9) \};\n`\\n the domain `= Domain(%);\n`\\n the range ` = \+ Range(%%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+Number_setG<+7$\"\"\" F'7$\"\"#\"\"%7$\"\"$\"\"*7$F*\"#;7$\"\"&\"#D7$\"\"'\"#O7$\"\"(\"#\\7$ \"\")\"#k7$F-\"#\")" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/%.|+~the~domai n~G<+\"\"\"\"\"#\"\"$\"\"%\"\"&\"\"'\"\"(\"\")\"\"*" }}{PARA 12 "" 1 " " {XPPMATH 20 "6#/%-|+~the~range~G<+\"\"\"\"\"%\"\"*\"#;\"#D\"#O\"#\\ \"#k\"#\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 110 "Number_set : = \{ seq([(k-3)^2, (k-5)^2], k = 1..7) \};\n`\\n the domain `= Domain( %);\n`\\n the range ` = Range(%%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%+Number_setG<)7$\"\"\"F'7$\"\"%\"#;7$F'\"\"*7$\"\"!F)7$F)F.7$F,F'7$F *F)" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/%.|+~the~domain~G<'\"\"!\"\"\" \"\"%\"\"*\"#;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/%-|+~the~range~G<' \"\"!\"\"\"\"\"%\"\"*\"#;" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 22 "3. Functions as Tables" }}{PARA 0 "" 0 "" {TEXT -1 149 "\nFunctions can \+ also be expressed as tables of values. The values of x from the domain are on the left, and values of y from the range are at right. \n" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 51 "f:= x -> 100-x^2:\narray( [[ k,f(k) ] $ k = \+ 0..8] );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7+7$\"\"!\"$+ \"7$\"\"\"\"#**7$\"\"#\"#'*7$\"\"$\"#\"*7$\"\"%\"#%)7$\"\"&\"#v7$\"\"' \"#k7$\"\"(\"#^7$\"\")\"#O" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "f:= x -> 2*floor(x/2):\narray( [[ k,f(k) ] $ k = 0..8] );" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7+7$\"\"!F(7$\"\"\"F(7$\" \"#F,7$\"\"$F,7$\"\"%F07$\"\"&F07$\"\"'F47$\"\"(F47$\"\")F8" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "f:= x -> 2^x + 1;\narray( [[ k, f(k)] $ k = 1..8] );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6# %\"xG6\"6$%)operatorG%&arrowGF(,&)\"\"#9$\"\"\"F0F0F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7*7$\"\"\"\"\"$7$\"\"#\"\"&7$F)\"\" *7$\"\"%\"#<7$F,\"#L7$\"\"'\"#l7$\"\"(\"$H\"7$\"\")\"$d#" }}}{PARA 0 " " 0 "" {TEXT -1 50 "\nThe values don't necessarily have to be integers ." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "f:= x -> :\narray( [[ k ,f(k) ] $ k = 0..8] );" }}{PARA 8 "" 1 "" {TEXT -1 22 "Error, `:` unex pected\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "f:= x -> evalf( sin(Pi/(x+3))):\narray( [[ k, f(k)] $ k = 1..8] );" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#-%'matrixG6#7*7$\"\"\"$\"+8y1rq!#57$\"\"#$\"+CD&y(eF+ 7$\"\"$$\"+-+++]F+7$\"\"%$\"+$RP)QVF+7$\"\"&$\"+DV$o#QF+7$\"\"'$\"+L9? ?MF+7$\"\"($\"+W*p,4$F+7$\"\")$\"+pbK " 0 "" {MPLTEXT 1 0 133 "f := x -> 3*x^2 -10*x + 21;\n`f(0)` = f(0);\n`f(1)` \+ = f(1);\n`f(-1)` = f(-1);\n`f(10)` = f(10);\n`f(100)` = f(100);\n`f(10 000)` = f(10000);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6 \"6$%)operatorG%&arrowGF(,(*&\"\"$\"\"\")9$\"\"#F/F/*&\"#5F/F1F/!\"\" \"#@F/F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%%f(0)G\"#@" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%%f(1)G\"#9" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%&f(-1)G\"#M" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%&f(10)G\"$@# " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%'f(100)G\"&@!H" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%)f(10000)G\"*@+!**H" }}}{PARA 0 "" 0 "" {TEXT -1 40 "\nFunctions come in all shapes and sizes." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 139 "f := x -> (x^2 + 11)/(3*x^2 - 9);\n`f(0)` = f(0 );\n`f(1)` = f(1);\n`f(-1)` = f(-1);\n`f(10)` = f(10);\n`f(100)` = f(1 00);\n`f(10000)` = f(10000);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG f*6#%\"xG6\"6$%)operatorG%&arrowGF(*&,&*$)9$\"\"#\"\"\"F2\"#6F2F2,&*& \"\"$F2F/F2F2\"\"*!\"\"F8F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%% f(0)G#!#6\"\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%%f(1)G!\"#" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/%&f(-1)G!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%&f(10)G#\"#P\"#(*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# /%'f(100)G#\"%PL\"%(***" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%)f(10000) G#\")PLLL\")(*******" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 132 "f \+ := x -> x - 3/(x^2 + 3);\n`f(0)` = f(0);\n`f(1)` = f(1);\n`f(-1)` = f( -1);\n`f(10)` = f(10);\n`f(100)` = f(100);\n`f(10000)` = f(10000);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arrow GF(,&9$\"\"\"*&\"\"$F.,&*$)F-\"\"#F.F.F0F.!\"\"F5F(F(F(" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#/%%f(0)G!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #/%%f(1)G#\"\"\"\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%&f(-1)G#!\" (\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%&f(10)G#\"%F5\"$.\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/%'f(100)G#\"((H+5\"&.+\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%)f(10000)G#\".(**H+++5\"*.+++\"" }}}{PARA 0 " " 0 "" {TEXT -1 89 "\nFunctions can also represent science formulas as well as abstract mathematical functions" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "Centigrade := F -> (5/9)*(F-32);\nCentigrade(0); Cent igrade( 212);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+CentigradeGf*6#%\" FG6\"6$%)operatorG%&arrowGF(,&*&#\"\"&\"\"*\"\"\"9$F1F1#\"$g\"F0!\"\"F (F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##!$g\"\"\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$+\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "Feet2Inches := inches -> inches * 12;\nFeet2Inches(1); Feet2Inches(2. 5); \nFeet2Inches(6); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,Feet2Inch esGf*6#%'inchesG6\"6$%)operatorG%&arrowGF(,$*&\"#7\"\"\"9$F/F/F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"$+$!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#s" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "Grams2Kg := grams -> grams*1000;\nG rams2Kg(3000); Grams2Kg(10); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)G rams2KgGf*6#%&gramsG6\"6$%)operatorG%&arrowGF(,$*&\"%+5\"\"\"9$F/F/F(F (F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"(+++$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"&++\"" }}}{PARA 0 "" 0 "" {TEXT -1 60 "\nNotice that \+ functions can also be evaluated with constants." }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 55 "f := x -> (x+3)/(x-5);\nf(6); f(15); f(Q); f(a ny_value);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)op eratorG%&arrowGF(*&,&9$\"\"\"\"\"$F/F/,&F.F/\"\"&!\"\"F3F(F(F(" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"*\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&%\"QG\"\"\"\"\"$ F&F&,&F%F&\"\"&!\"\"F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&%*any_va lueG\"\"\"\"\"$F&F&,&F%F&\"\"&!\"\"F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "f := x -> 100*x^3 + 2000*x + 3000;\nf(6); f(15); f(Q ); f(any_value);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\" 6$%)operatorG%&arrowGF(,(*&\"$+\"\"\"\")9$\"\"$F/F/*&\"%+?F/F1F/F/\"%+ IF/F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"&+m$" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#\"'+0P" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&\"$+\" \"\"\")%\"QG\"\"$F&F&*&\"%+?F&F(F&F&\"%+IF&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&\"$+\"\"\"\")%*any_valueG\"\"$F&F&*&\"%+?F&F(F&F&\" %+IF&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{PARA 0 "" 0 "" {TEXT 259 36 "\n \251 2002 Waterloo Maple Inc " }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}}{MARK "7 2 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }