{VERSION 4 0 "IBM INTEL NT" "4.0" } {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 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 "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 } {PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 8 2 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 3" 4 5 1 {CSTYLE "" -1 -1 "" 1 12 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 0 0 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 0 }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 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 18 "M odule 1 : Algebra" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 3 "" 0 "" {TEXT -1 15 "104 : Functions" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 89 "_______________ ______________________________________________________________________ ____" }}{PARA 4 "" 0 "" {TEXT -1 20 "A. Function Notation" }}{PARA 0 " " 0 "" {TEXT -1 89 "__________________________________________________ _______________________________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 19 "FU NCTION DEFINITION" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 402 "The way you define functions in Maple is slightly differ ent that what you might expect. This underscores the fact that a funct ion is more than just a formula. The concept of a function is a proces s that takes one number (x, the independent variable ) is transforms i t into another (y, the dependent variable) , often by way of a formula . Maple reinforces the idea of the transformation by its notation." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "f := x -> 3*x^2 + x + 7;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG R6#%\"xG6\"6$%)operatorG%&arrowGF(,(*$)9$\"\"#\"\"\"\"\"$F/F1\"\"(F1F( F(F(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 54 " Here is another function - this time a linear function" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "g := x \+ -> 12*x - 31;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGR6#%\"xG6\"6$%) operatorG%&arrowGF(,&9$\"#7\"#J!\"\"F(F(F(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 19 "FUNCTION EVALUATION" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 120 "Once you have \+ defined the function, you can evaluate it with large and small numbers , fractions, and irrational numbers." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "f(1); f(10000);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"#6" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#\"*2+,+$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "f(4/5); f(7 +3/11);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"$V#\"#D" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"&F4#\"$@\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "f(sqrt(17)); f(.00004);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&\"#e\"\"\"*$-%%sqrtG6#\"# " 0 "" {MPLTEXT 1 0 17 "f(a); f(R - T); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)%\"aG\"\"#\"\"\"\"\"$F&F(\"\" (F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**$),&%\"RG\"\"\"%\"TG!\"\"\" \"#F(\"\"$F'F(F)F*\"\"(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "f(x-3); f( f(x) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$),&%\" xG\"\"\"\"\"$!\"\"\"\"#F(F)F'F(\"\"%F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**$),(*$)%\"xG\"\"#\"\"\"\"\"$F)F+\"\"(F+F*F+F,*&F,F+F(F+F+F)F+ \"#9F+" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 61 "A1 \+ Define the function g(x) : = x/(x-3) and evaluate it \n" }}{PARA 0 "" 0 "" {TEXT -1 248 "\011A. Determine the value of g(0), g(4), g(2), \+ and g(3). \n\011B. Why didnt you get an answer for g(3)?\n \011C. Evaluate g(2.9999) and g(3.0001), and make a guess about g(3); \n\011D. g(1,000,000) \011(Remember : Do not type commas in number s in Maple)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 89 "_______________________________ __________________________________________________________" }}{PARA 4 "" 0 "" {TEXT -1 17 "B. Domain & Range" }}{PARA 0 "" 0 "" {TEXT -1 89 "_____________________________________________________________________ ____________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 195 "There are several ways to see what a function does to a \+ finite set of numbers. Here we define a domain of integers, and then a pply the function to each member of the domain using the map command. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 27 "- Her e we define a function" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "f := x -> 3*x^2 + x + 7;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6#%\"xG6\"6$%)operatorG%&arrowGF(,(*$ )9$\"\"#\"\"\"\"\"$F/F1\"\"(F1F(F(F(" }}}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 36 "- a domain consisting of a sequence, " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "Domain := [ k $ k = -10..10 ];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'DomainG77!#5!\"*!\")!\"(!\"'!\"&!\"%!\"$!\"#!\"\"\"\"!\"\"\" \"\"#\"\"$\"\"%\"\"&\"\"'\"\"(\"\")\"\"*\"#5" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 72 "- and create a range by a pplying or 'mapping' the function to the domain" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "Range := map ( f, Domain);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&RangeG77\"$(H\"$T #\"$\">\"$Z\"\"$4\"\"#x\"#^\"#J\"#<\"\"*\"\"(\"#6\"#@\"#P\"#f\"#()\"$@ \"\"$h\"\"$2#\"$f#\"$<$" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 190 "An even nicer way to view what a function does to see how it transforms different numbers at once. To do this, we will \+ create an array where we can see the domain and range at the same time ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 51 "- Th e value of k from 1 to 10 will be the x values." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "array( [[ k, f(k) ] $ k = 1..10] );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6# 7,7$\"\"\"\"#67$\"\"#\"#@7$\"\"$\"#P7$\"\"%\"#f7$\"\"&\"#()7$\"\"'\"$@ \"7$\"\"(\"$h\"7$\"\")\"$2#7$\"\"*\"$f#7$\"#5\"$<$" }}}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 5 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 205 "It may be easier for you to see the entire array at once , if you change the viewing size by going to the VIEW menu, and select ZOOM FACTOR, then 75%. There are also key commands to change the zoom setting." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 141 "B 1. Define the function f(x) = 1/x2, copy and paste the map and array \+ commands above and re-execute them to see the affect of this function. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 3 "B2." }}{PARA 0 "" 0 "" {TEXT -1 457 " \+ \011A. Create an array for the functions x4, (x-1)4, (x-2)4 for the domain of numbers :\n\011\011 -8, -7, ...-2,-1,0,1,2,...,7 ,8 by defining f(x) = x4 and using the command\n > array ( [[ f(k), f(k-1), f(k-2) ] $ k = 8..8] );\n\011 B. How are the numbers in the first two columns related?\n \011C. How are the numbers in the last two columns related?\n\011 D. Can you gues s what the numbers of the form (x-3)^4 would look like?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 89 "_________________________ ________________________________________________________________" }} {PARA 4 "" 0 "" {TEXT -1 37 "C. Function Operations and Composites" }} {PARA 0 "" 0 "" {TEXT -1 89 "_________________________________________ ________________________________________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 147 "You can also combine functions algebraically in a number of ways. First we define two functions, f(x ) and g(x) to use in our unethical experiments." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "f := x -> 1 \+ +2/x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6#%\"xG6\"6$%)operator G%&arrowGF(,&\"\"\"F-*&\"\"#F-9$!\"\"F-F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "g := x -> x/(x-3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGR6#%\"xG6\"6$%)operatorG%&arrowGF(*&9$\"\"\",&F-F.\"\"$!\" \"F1F(F(F(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 64 "First, we'll compute the sum of the functions. We are using the " }{TEXT 256 9 "simplify " }{TEXT -1 95 " command to simplify the res ult. The % key is a shortcut for the most recently computed result." } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 98 "What you see in the output is the original and the simplified version of the s um of f(x) and g(x)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "f(x) + g(x); simplify(%);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#,(\"\"\"F$*&\"\"#F$%\"xG!\"\"F$*&F'F$,&F'F$\"\"$ F(F(F$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,(*$)%\"xG\"\"#\"\"\"F(F'! \"\"\"\"'F*F)*&F'F),&F'F)\"\"$F*F)F*" }}}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 330 "Now, we look at the sum, difference, product, and quotient of two functions. These operations are performe d exactly the same way that you would do them with numbers using the + ,-,*, and / keys for add, substract, multiply and divide. the way we a re doing it in Maple here is slightly more complicated but the output \+ is much nicer." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "f(x) + g(x): % = simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,(\"\"\"F%*&\"\"#F%%\"xG!\"\"F%*&F(F%,&F(F%\"\"$F )F)F%*&,(*$)F(F'F%F'F(F)\"\"'F)F%*&F(F%F+F%F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "f(x) - g(x): % = simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,(\"\"\"F%*&\"\"#F%%\"xG!\"\"F%*&F(F%,&F(F%\"\"$F )F)F),$*&,&F(F%\"\"'F%F%*&F(F%F+F%F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "f(x) * g(x): % = simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&*&,&\"\"\"F'*&\"\"#F'%\"xG!\"\"F'F'F*F'F',&F*F'\"\"$ F+F+*&,&F*F'F)F'F'F,F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "f (x) / g(x); % = simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&*& ,&\"\"\"F&*&\"\"#F&%\"xG!\"\"F&F&,&F)F&\"\"$F*F&F&F)F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&*&,&\"\"\"F'*&\"\"#F'%\"xG!\"\"F'F',&F*F'\"\"$F +F'F'F*F+*&*&,&F*F'F)F'F'F,F'F'*$)F*F)F'F+" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 56 "We can also compute a \"linear \+ combination\" of functions." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "7*f(x) + 12*g(x): % = simplify(%) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,(\"\"(\"\"\"*&\"#9F&%\"xG!\"\"F &*&*&\"#7F&F)F&F&,&F)F&\"\"$F*F*F&*&,(*$)F)\"\"#F&\"#>*&F%F&F)F&F*\"#U F*F&*&F)F&F.F&F*" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 43 "...and even compositioned of the functions." }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "f(g(x )): % = simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&\"\"\"F%* &*&\"\"#F%,&%\"xGF%\"\"$!\"\"F%F%F*F,F%,$*&,&F*F%F(F,F%F*F,F+" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "g(f(x)): % = simplify(%); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&,&\"\"\"F&*&\"\"#F&%\"xG!\"\"F& F&,&!\"#F&*&F(F&F)F*F&F*,$*&,&F)F&F(F&F&,&F)F&F&F*F*#F*F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "f(f(x)): % = simplify(%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/,&\"\"\"F%*&\"\"#F%,&F%F%*&F'F%%\"xG! \"\"F%F+F%*&,&F*\"\"$F'F%F%,&F*F%F'F%F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "g(g(x)): % = simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&%\"xG\"\"\"*&,&F%F&\"\"$!\"\"F&,&*&F%F&F(F*F&F)F*F&F *,$*&F%F&,&F%\"\"#\"\"*F*F*F*" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 96 "C1 Define the \+ functions f(x) = 3x2 + x + 7 and g(x) = (x+1)/(x-2), then compute and simplify \n" }}{PARA 0 "" 0 "" {TEXT -1 487 "\011A. f(x) + g(x) \+ \011B. f(g(x)) \+ \011 \011 C. 20g(x) + 1/f(x) \n\011D. g(f(x ))\011\011 E. f (f(x) + g(x) \+ ) \011F. f(g( f(x) )) \n\011G . g( 1/f(x) ) \011 H. f(x+3) - f(x -3)\011 \011 I. (g(x+h) -g(x) )/h\n \011J. (f(x)-f(a))/(x-a) \011K. (f(g(x)) f(g(a)) ) / (x - a)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 89 "_________________________________________________________ ________________________________" }}{PARA 4 "" 0 "" {TEXT -1 21 "D. Ve rtical Line Test" }}{PARA 0 "" 0 "" {TEXT -1 89 "_____________________ ____________________________________________________________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 388 "When you are looking at the graph of a relation, the way to determine if its a function or not is to use the \"Vertical Line Test\" : If any vertica l line crosses the graph in two or more places, the relation is not a \+ function. The following commands are a little more advanced. Don't wor ry about understanding all of the Maple, concentrate on the mathematic al meaning of the graph you see." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "expr := 4*x^2 - 3*y^2 + y^3 \+ = 1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%exprG/,(*$)%\"xG\"\"#\"\"\" \"\"%*&\"\"$F+)%\"yGF*F+!\"\"*$)F0F.F+F+F+" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 165 "plots[display](\n implicitplot( expr ,x=-2..2, y=-2..4,co lor = blue, thickness = 2),\n implicitplot( \{seq(x = k/4, k=-8..8 )\}, x=-2..2, y= -2..4, color = red));" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "65-%'CURVESG6fs7$7$$!\"#\"\"!$!3QBckuWmrF-$!3Us_NCy%zw\"F-7$7$$!3ILLLL3P$)>F-$!3-++++++g_8:F-7$7 $$!3;++++++!o\"F-$!3:Ls2lzE4:F-FU7$Fen7$$!33;rr`/H%e\"F-$!3:EVU>VcB9F- 7$7$$!3C++++++?:F-$!3U.W*\\2&*fO\"F-F[o7$Fao7$$!3c8]skmq#[\"F-$!3;![7H +SfL\"F-7$7$$!3TWWWWWH89F-$!3-++++++!G\"F-Fgo7$F]p7$$!3KJL\"o2)*=Q\"F- $!3_.+y%)G:Z7F-7$7$$!3K++++++g8F-$!3z\\+j_HCC7F-Fcp7$7$Fjp$!3c\\+j_HCC 7F-7$$!3Cn[2w'yTG\"F-$!3w*p()e)>t`6F-7$7$$!3Q+++++++7F-$!3k\"[%Q(**[a2 \"F-Fbq7$Fhq7$$!3))*3klwyY=\"F-$!3qlQ:]=)H1\"F-7$7$$!3C9dG9dVc6F-$!3/+ +++++S5F-F^r7$Fdr7$$!3Y6j\"3D8&*3\"F-$!3)oLbxB,tl*!#=7$7$$!3[++++++S5F -$!3)*zI)[;3y5*F_sFjr7$7$Fbs$\"3alExQms([\"F-7$$!3')*********\\(o5F-$ \"3')*************f\"F-7$Fjs7$$!3[E'45I-y2\"F-$\"3wQW^^Mqc;F-7$7$$!3R& G9dGkq5\"F-$\"3&)************R=F-F`t7$Fft7$$!3#**Hu,UQ'46F-$\"3d\\9EIw XW>F-7$7$$!3fr&G9dyH6\"F-$\"33++++++!3#F-F\\u7$Fbu7$$!3Sd!fag_'*4\"F-$ \"3Y&e)=3*y%p@F-7$7$$!3_9dG9dBx5F-$\"3G++++++?BF-Fhu7$F^v7$$!3USJLGQ:k 5F-$\"3k5(*\\U2BcBF-7$7$Fbs$\"3x,)*>=c7BCF-Fdv7$Fas7$$!3gSil2P1[**F_s$ !3uYc^QW!zn)F_s7$7$$!30nmmmmTN#*F_s$!3U+++++++!)F_sF^w7$Fdw7$$!3k'=?Ys #G5!*F_s$!3wF(pI\"fd%o(F_s7$7$$!3[/++++++))F_s$!3g&o=g8f**Q(F_sFjw7$7$ Fax$\"379m^Y-pK5F-7$$!3_mmmmmTR\"*F_s$\"3*)************>6F-7$7$$!3jnmm mmTR\"*F_sF\\y7$$!3a_@\"*HJ@`&*F_s$\"3/Ao[p>)HB\"F-7$7$$!3_mmmm;%=+\"F -$\"3))************f8F-Fby7$7$Fiy$\"35++++++g8F-7$Fbs$\"3wlExQms([\"F- 7$Fjv7$$!354nlKum/5F-$\"3@j])*[6+2DF-7$7$$!3elmmmmTB)*F_s$\"3]++++++gD F-Fez7$F[[l7$$!3%\\)oAb\\D%H*F_s$\"3dKSGV#QTj#F-7$7$$!3O.++++++))F_s$ \"3L')ytseQ.FF-Fa[l7$7$Fh[lFcx7$$!3gsx#em&)*G\")F_s$!3qY$e7]@lg'F_s7$7 $$!3e+++++!pE(F_s$!3a+++++++cF_sF^\\l7$Fd\\l7$$!3i\"RWm>\\!QsF_s$!3:BQ\\MI%F_s7$7$$!3s++++]7ndF_s$! 3i+++++++KF_sFf_l7$F\\`l7$$!3.\"QdYx_,s&F_s$!3vLR,Q3x>IF_s7$7$$!3'Q+++ +++g&F_s$!3KJ>g(*HveDF_sFb`l7$7$Fi`l$\"3E)>6]3Y-(GF_s7$$!3\"********* \\i:fF_s$\"37**************RF_s7$Faal7$$!3))*o&)\\t@Gc'F_s$\"39G&yCgKU W&F_s7$7$$!39********\\7\"*pF_s$\"3-*************R'F_sFgal7$F]bl7$Fa]l $\"3G1q:yZ?!y'F_s7$7$$!31.++++++sF_sFc_l7$$!31,-cV \"HF-7$7$Fi`l$\"3)Q-$>JJqiHF-Fjbl7$7$Fi`l$!3wI>g(*HveDF_s7$$!3917gbqC) >&F_s$!3t'>)f;%HES\"F_s7$7$$!3YLLLLL$)))\\F_s$!372++++++!)!#>Fgcl7$F]d l7$$!3#ylNEaq@3&F_s$\"3'o![`R\"eDB)Fbdl7$7$$!3pKLLLL$o7&F_s$\"3?****** *******f\"F_sFddl7$FjdlF^al7$F`cl7$$!38$yfg6Z(3_F_s$\"3qn*3u178)HF-7$7 $$!3c.++++++SF_s$\"3ffpG7I!)QIF-Fael7$Fgel7$$!3OCs)ee7M*RF_s$\"3&Q3$)y )=,RIF-7$7$$!3')e*******\\A'RF_s$\"3#4++++++/$F-F]fl7$Fcfl7$$!3yov^B_k 4EF_s$\"3cNw_$yY92$F-7$7$$!3_.++++++CF_s$\"3A)*f'p$3KwIF-Fifl7$F_gl7$$ !3!**[dNT+)R6F_s$\"3cBO.i+(44$F-7$7$$!3)[.++++++)Fbdl$\"3%Rpr83?\\4$F- Fegl7$7$F\\hl$\"3Q%pr83?\\4$F-7$$\"3>$3()=Ch'QVFbdlFbhl7$7$$\"3[l***** *******zFbdlF^hlFdhl7$7$FihlFbhl7$$\"3:$et\"*o>v8#F_s$\"3oiRiY?PzIF-7$ 7$$\"3e'************R#F_sFbglF]il7$7$$\"3)o*************RF_sFjel7$$\"3 ?_*******\\A'RF_sFffl7$Fjil7$Fdil$\"3o)*f'p$3KwIF-7$7$$\"3?(********** **f&F_s$!354>g(*HveDF_s7$$\"3YLLLLL$)))\\F_sF`dl7$Fgjl7$$\"3],]G^4OP]F _s$\"3K,#\\sIdeR%!#?7$7$$\"3pKLLLL$o7&F_sF]elF[[m7$Fb[m7$$\"3Q%Qb3![W' H&F_s$\"3K(F_s$!3/W,N'ybwY&F_s7$$\"3i********\\7ndF_sF_`l7$F_]m7$Fcj l$!3m4>g(*HveDF_s7$F\\\\m7$$\"3H;-hpzTAeF_s$\"3[qYeXIPmOF_s7$7$$\"3\"* ********\\i:fF_sFdalFg]m7$F]^m7$$\"3xYmUn#>>V'F_s$\"3+B+'))4@@:&F_s7$7 $$\"39********\\7\"*pF_sF`blFa^m7$Fg^m7$$\"3kkQ7@\"*[&3(F_s$\"3W*>9$=j wrlF_s7$7$F[]m$\"3u!*p:yZ?!y'F_sF[_m7$7$FcjlFacl7$$\"3UE\")3NVu#\\'F_s $\"3K\"yO(\\$)31HF-7$7$F[]m$\"3#oxnIiO7'GF-Ff_m7$7$F\\^l$!3#yn=g8f**Q( F_s7$$\"3Y***********oE(F_sFg\\l7$Fc`mFj\\m7$7$$\"3S'************>(F_s Fb_m7$$\"3x;CN`2+NxF_s$\"3/q8(*p))\\(*zF_s7$7$$\"3!***********p(3)F_sF \\^lF[am7$Faam7$$\"3k(=!Ht$Q4Q)F_s$\"3`7Z1SCfG%*F_s7$7$$\"3q'********* ***z)F_s$\"3c7m^Y-pK5F-Feam7$7$$\"3!y************z)F_s$\"3A()ytseQ.FF- 7$$\"3q&*********\\szF_sFi^l7$FfbmF\\`m7$7$$\"3\")************R5F-$!3K tI)[;3y5*F_s7$$\"30nmmmmTN#*F_sFgw7$F`cm7$F\\bmFa`m7$7$FbbmF^bm7$$\"3 \"\\nN6j'R9!*F_s$\"3[['H`]Sy3\"F-7$7$$\"3_mmmmmTR\"*F_sF\\yFgcm7$7$$\" 3TlmmmmTR\"*F_sF\\y7$$\"3=k<^iBR'e*F_s$\"3)\\BBc9T?C\"F-7$7$$\"3_mmmm; %=+\"F-F[zFddm7$Fjdm7$$\"3&)yhbM)\\O,\"F-$\"3UJd;[__*R\"F-7$7$F\\cm$\" 3KjExQms([\"F-F^em7$7$F\\cm$\"3l-)*>=c7BCF-7$$\"3OjmmmmTB)*F_sF^[l7$F[ fmFabm7$7$$\"3s*************>\"F-$!3'4[%Q(**[a2\"F-7$$\"3C9dG9dVc6F-Fg r7$7$$\"3Y9dG9dVc6F-FgrF[cm7$Fdem7$$\"3[:JN8:xg5F-$\"3/E.(*HF%)o:F-7$7 $$\"3')*********\\(o5F-F]tF]gm7$Fcgm7$$\"3!\\u3tZ2T4\"F-$\"3A#)o.%yQ)e F-7$7$$\"3fr&G9dyH6\"F-FeuFahm7$Fghm7$$\"3=6LSam%z3\"F-$\"3#H.&R=+3[AF -7$7$$\"3I9dG9dBx5F-FavF[im7$7$$\"339dG9dBx5F-FavFhem7$F`fm7$$\"3ivyq, r=i7F-$!3*R\"=c_1GL6F-7$7$$\"3m************f8F-$!3!*[+j_HCC7F-Fiim7$7$ $\"3d************>:F-$!3)HS%*\\2&*fO\"F-7$$\"3TWWWWWH89F-F`p7$FjjmF_jm 7$Fejm7$$\"3K)\\,>tZAm\"F-$!3Q[A&yfrL\\\"F-7$7$$\"3[************z;F-$! 3rKs2lzE4:F-F_[n7$7$$\"3T************R=F-$!3/cI)[lKrj\"F-7$$\"3kaaaaa* 3p\"F-FR7$F`\\nFe[n7$7$$\"3M**************>F-$!3sAckuWmrF-F77$Fj\\nF[\\n-%'COLOURG6&%$RGBG$F*F*Fb]n$\"*++++\"!\")-%*THICK NESSG6#\"\"#-F$6U7$7$$\"3qX9y!yyxQ\"!#MF(7$$\"3QGs!R!R*)Qp!#N$!3y+++++ +!)=F-7$7$Fb^n$!3C++++++g&F_s7$7$Fb^nF`blF^cn7$7$F^^nF`bl7 $Fb^n$\"3a%************f(F_s7$7$Fb^nF\\^lFecn7$7$F^^nF\\^l7$Fb^n$\"2M* **************F-7$7$Fb^nF\\yF\\dn7$7$F^^nF\\y7$Fb^n$\"3L************R7 F-7$7$Fb^nF[zFcdn7$7$F^^nF[z7$Fb^n$\"3a************z9F-7$7$Fb^n$\"33++ +++++;F-Fjdn7$7$F^^nF]t7$Fb^n$\"3J************>F-7$7$Fb^nFeuFjen7$7$F^^nFeu7$Fb^n$\"3s *************>#F-7$7$Fb^nFavFafn7$7$F^^nFav7$Fb^n$\"3%*************RCF -7$7$Fb^nF^[lFhfn7$7$F^^nF^[l7$Fb^n$\"3g++++++!o#F-7$7$Fb^nFi^lF_gn7$7 $F^^nFi^l7$Fb^n$\"3P++++++?HF-7$7$Fb^nFfflFfgn7$7$F^^nFffl7$Fb^n$\"3e+ +++++gJF-7$7$Fb^n$\"39,+++++!G$F-F]hn7$7$F^^nFbhn7$Fb^n$\"3C,++++++MF- 7$7$Fb^n$\"3N,+++++?NF-Ffhn7$7$F^^nF[in7$Fb^n$\"3,,+++++SOF-7$7$Fb^n$ \"3c,+++++gPF-F_in7$7$F^^nFdin7$Fb^n$\"3m,+++++!)QF-7$7$Fb^n$\"3y,++++ ++SF-Fhin-F_]n6&Fa]nFc]nFb]nFb]n-F$6U7$7$$\"3++++++++]F_sF(7$Fejn$!3O+ +++++5>F-7$7$FejnF7Fgjn7$7$FejnFi^n7$Fejn$!3O++++++q;F-7$7$FejnFRF^[o7 $Fb[o7$Fejn$!3Q++++++I9F-7$7$Fejn$!3!)************z7F-Fd[o7$7$FejnF`p7 $Fejn$!3Q++++++!>\"F-7$7$FejnFgrF]\\o7$Fa\\o7$Fejn$!3)R++++++]*F_s7$7$ FejnFgwFc\\o7$Fg\\o7$Fejn$!33/++++++rF_s7$7$FejnFg\\lFi\\o7$F]]o7$Fejn $!3u/++++++ZF_s7$7$FejnF_`lF_]o7$Fc]o7$Fejn$!3#[++++++I#F_s7$7$FejnF`d lFe]o7$Fi]o7$Fejn$\"2a\\*************Fbdl7$7$FejnF]elF[^o7$F_^o7$Fejn$ \"3s%************\\#F_s7$7$FejnFdalFa^o7$Fe^o7$Fejn$\"3O%************* [F_s7$7$FejnF`blFg^o7$F[_o7$Fejn$\"3G%************H(F_s7$7$FejnF\\^lF] _o7$Fa_o7$Fejn$\"3=%************p*F_s7$7$FejnF\\yFc_o7$Fg_o7$Fejn$\"3_ ************47F-7$7$FejnF[zFi_o7$F]`o7$Fejn$\"3G************\\9F-7$7$F ejn$\"3k*************f\"F-F_`o7$Fc`o7$Fejn$\"3G*************o\"F-7$7$F ejnFitFg`o7$F[ao7$Fejn$\"3\\************H>F-7$7$FejnFeuF]ao7$Faao7$Fej n$\"3#*************p@F-7$7$FejnFavFcao7$Fgao7$Fejn$\"39++++++5CF-7$7$F ejnF^[lFiao7$F]bo7$Fejn$\"3#*************\\EF-7$7$FejnFi^lF_bo7$Fcbo7$ Fejn$\"37++++++!*GF-7$7$FejnFfflFebo7$Fibo7$Fejn$\"3M++++++IJF-7$7$Fej nFbhnF[co7$F_co7$Fejn$\"3a++++++qLF-7$7$FejnF[inFaco7$Feco7$Fejn$\"3@, +++++5OF-7$7$FejnFdinFgco7$F[do7$Fejn$\"3)4++++++&QF-7$7$FejnF]jnF]doF _jn-F$6U7$7$$\"3+++++++]F-7$7$FfdoFeuF^[p7$Fb[p7$Ffdo$\"3T***********\\@#F-7$7$FfdoFavF d[p7$Fh[p7$Ffdo$\"3i***********\\X#F-7$7$FfdoF^[lFj[p7$F^\\p7$Ffdo$\"3 #)***********\\p#F-7$7$FfdoFi^lF`\\p7$Fd\\p7$Ffdo$\"30++++++NHF-7$7$Ff doFfflFf\\p7$Fj\\p7$Ffdo$\"3E++++++vJF-7$7$FfdoFbhnF\\]p7$F`]p7$Ffdo$ \"3[++++++:MF-7$7$FfdoF[inFb]p7$Ff]p7$Ffdo$\"3E++++++bOF-7$7$FfdoFdinF h]p7$F\\^p7$Ffdo$\"3Y++++++&*QF-7$7$FfdoF]jnF^^pF_jn-F$6U7$7$$\"\"\"F* F(7$Fg^p$!3R++++++S>F-7$7$Fg^pF;Fi^p7$F]_p7$Fg^p$!3;+++++++#F_s7$7$Fg^pFd alF_bp7$Fcbp7$Fg^p$\"3I'************f%F_s7$7$Fg^pF`blFebp7$Fibp7$Fg^p$ \"3A'*************pF_s7$7$Fg^pF\\^lF[cp7$F_cp7$Fg^p$\"37'************R *F_s7$7$Fg^pF\\yFacp7$Fecp7$Fg^p$\"3q************z6F-7$7$Fg^pF[zFgcp7$ F[dp7$Fg^p$\"3[************>9F-7$7$Fg^pF_enF]dp7$Fadp7$Fg^p$\"3q****** ******f;F-7$7$Fg^pFitFcdp7$Fgdp7$Fg^p$\"3Y**************=F-7$7$Fg^pFeu Fidp7$F]ep7$Fg^p$\"3o************R@F-7$7$Fg^pFavF_ep7$Fcep7$Fg^p$\"3)) ************zBF-7$7$Fg^pF^[lFeep7$Fiep7$Fg^p$\"36++++++?EF-7$7$Fg^pFi^ lF[fp7$F_fp7$Fg^p$\"3w++++++gGF-7$7$Fg^pFfflFafp7$Fefp7$Fg^p$\"3_+++++ ++JF-7$7$Fg^pFbhnFgfp7$F[gp7$Fg^p$\"3u++++++SLF-7$7$Fg^pF[inF]gp7$Fagp 7$Fg^p$\"3S,+++++!e$F-7$7$Fg^pFdinFcgp7$Fggp7$Fg^p$\"3<,+++++?QF-7$7$F g^pF]jnFigpF_jn-F$6U7$7$$\"3++++++++vF_sF(7$Fbhp$!3Q++++++0=F-7$7$Fbhp F7Fdhp7$Fhhp7$Fbhp$!3S++++++l:F-7$7$FbhpFRFjhp7$F^ip7$Fbhp$!3S++++++D8 F-7$7$FbhpF`pF`ip7$Fdip7$Fbhp$!3S++++++&3\"F-7$7$FbhpFgrFfip7$Fjip7$Fb hp$!3=/+++++]%)F_s7$7$FbhpFgwF\\jp7$F`jp7$Fbhp$!3E/+++++]gF_s7$7$FbhpF g\\lFbjp7$Ffjp7$Fbhp$!3O/+++++]OF_s7$7$FbhpF_`lFhjp7$F\\[q7$Fbhp$!3W/+ ++++]7F_s7$7$FbhpF`dlF^[q7$Fb[q7$Fbhp$\"3i&***********\\6F_s7$7$FbhpF] elFd[q7$Fh[q7$Fbhp$\"3Q&***********\\NF_s7$7$FbhpFdalFj[q7$F^\\q7$Fbhp $\"3I&***********\\fF_s7$7$FbhpF`blF`\\q7$Fd\\q7$Fbhp$\"3?&*********** \\$)F_s7$7$FbhpF\\^lFf\\q7$Fj\\q7$Fbhp$\"3_***********\\2\"F-7$7$FbhpF \\yF\\]q7$F`]q7$Fbhp$\"3]***********\\J\"F-7$7$FbhpF[zFb]q7$Ff]q7$Fbhp $\"3]***********\\b\"F-7$7$FbhpF]tFh]q7$F\\^q7$Fbhp$\"3[***********\\z \"F-7$7$FbhpFitF^^q7$Fb^q7$Fbhp$\"3q***********\\.#F-7$7$FbhpFeuFd^q7$ Fh^q7$Fbhp$\"3#************\\F#F-7$7$FbhpFavFj^q7$F^_q7$Fbhp$\"37+++++ +:DF-7$7$FbhpF^[lF`_q7$Fd_q7$Fbhp$\"3M++++++bFF-7$7$FbhpFi^lFf_q7$Fj_q 7$Fbhp$\"3a++++++&*HF-7$7$FbhpFfflF\\`q7$F``q7$Fbhp$\"3@,+++++NKF-7$7$ FbhpFbhnFb`q7$Ff`q7$Fbhp$\"3a++++++vMF-7$7$FbhpF[inFh`q7$7$Fbhp$\"3\"4 ++++++_$F-7$Fbhp$\"3v++++++:PF-7$7$FbhpFdinFaaq7$Feaq7$Fbhp$\"3S,+++++ bRF-7$7$FbhpF]jnFgaqF_jn-F$6U7$7$$!3++++++++DF_sF(7$F`bq$!3a++++++&)>F -7$7$F`bqF7Fbbq7$Ffbq7$F`bq$!3b++++++XF-7$7$FhbrFeuFjhr7$F^ir7$Fhbr$\"3/++++++&=#F-7$7$FhbrFavF`ir7$F dir7$Fhbr$\"3F++++++DCF-7$7$FhbrF^[lFfir7$Fjir7$Fhbr$\"3/++++++lEF-7$7 $FhbrFi^lF\\jr7$F`jr7$Fhbr$\"3p++++++0HF-7$7$FhbrFfflFbjr7$Ffjr7$Fhbr$ \"3\"4+++++]9$F-7$7$FhbrFbhnFhjr7$F\\[s7$Fhbr$\"3o++++++&Q$F-7$7$FhbrF [inF^[s7$Fb[s7$Fhbr$\"3L,+++++DOF-7$7$FhbrFdinFd[s7$Fh[s7$Fhbr$\"35,++ +++lQF-7$7$FhbrF]jnFj[sF_jn-F$6U7$7$$!3++++++++:F-F(7$Fc\\s$!3[++++++! z\"F-7$7$Fc\\sFi^nFe\\s7$Fi\\s7$Fc\\s$!3E++++++]:F-7$7$Fc\\sFRF[]s7$F_ ]s7$Fc\\s$!3]++++++58F-7$7$Fc\\sF`pFa]s7$Fe]s7$Fc\\s$!3G++++++q5F-7$7$ Fc\\sFgrFg]s7$F[^s7$Fc\\s$!390++++++$)F_s7$7$Fc\\sFgwF]^s7$Fa^s7$Fc\\s $!37/++++++fF_s7$7$Fc\\sFg\\lFc^s7$Fg^s7$Fc\\s$!3w/++++++NF_s7$7$Fc\\s F_`lFi^s7$F]_s7$Fc\\s$!3W/++++++6F_s7$7$Fc\\sF`dlF__s7$Fc_s7$Fc\\s$\"3 e&************H\"F_s7$7$Fc\\sF]elFe_s7$Fi_s7$Fc\\s$\"3]&************p$ F_s7$7$Fc\\sFdalF[`s7$F_`s7$Fc\\s$\"3U&************4'F_s7$7$Fc\\sF`blF a`s7$Fe`s7$Fc\\s$\"3K&************\\)F_s7$7$Fc\\sF\\^lFg`s7$F[as7$Fc\\ s$\"3k*************3\"F-7$7$Fc\\sF\\yF]as7$Faas7$Fc\\s$\"3T*********** *H8F-7$7$Fc\\sF[zFcas7$Fgas7$Fc\\s$\"3i************p:F-7$7$Fc\\sF]tFia s7$F]bs7$Fc\\s$\"3R************4=F-7$7$Fc\\sFitF_bs7$Fcbs7$Fc\\s$\"3Q* ***********\\?F-7$7$Fc\\sFeuFebs7$Fibs7$Fc\\s$\"3/++++++!H#F-7$7$Fc\\s FavF[cs7$F_cs7$Fc\\s$\"3D++++++IDF-7$7$Fc\\sF^[lFacs7$Fecs7$Fc\\s$\"3Y ++++++qFF-7$7$Fc\\sFi^lFgcs7$F[ds7$Fc\\s$\"3n++++++5IF-7$7$Fc\\sFfflF] ds7$Fads7$Fc\\s$\"3!4++++++D$F-7$7$Fc\\sFbhnFcds7$Fgds7$Fc\\s$\"35,+++ ++!\\$F-7$7$Fc\\sF[inFids7$F]es7$Fc\\s$\"3J,+++++IPF-7$7$Fc\\sFdinF_es 7$Fces7$Fc\\s$\"33,+++++qRF-7$7$Fc\\sF]jnFeesF_jn-F$6U7$7$$!3+++++++]7 F-F(7$F^fs$!3r++++++D>F-7$7$F^fsFi^nF`fs7$Fdfs7$F^fs$!3s++++++&o\"F-7$ 7$F^fsFRFffs7$Fjfs7$F^fs$!3]++++++X9F-7$7$F^fsF`pF\\gs7$F`gs7$F^fs$!3_ ++++++07F-7$7$F^fsFgrFbgs7$Ffgs7$F^fs$!3C0+++++]'*F_s7$7$F^fsFgwFhgs7$ F\\hs7$F^fs$!3W1+++++]sF_s7$7$F^fsFg\\lF^hs7$Fbhs7$F^fs$!3)f++++++&[F_ s7$7$F^fsF_`lFdhs7$Fhhs7$F^fs$!311+++++]CF_s7$7$F^fsF`dlFjhs7$F^is7$F^ fs$!3)ej++++++&F`[m7$7$F^fsF]elF`is7$Fdis7$F^fs$\"3w$***********\\BF_s 7$7$F^fsFdalFfis7$Fjis7$F^fs$\"37$***********\\ZF_s7$7$F^fsF`blF\\js7$ F`js7$F^fs$\"39%***********\\rF_s7$7$F^fsF\\^lFbjs7$Ffjs7$F^fs$\"31%** *********\\&*F_s7$7$F^fsF\\yFhjs7$F\\[t7$F^fs$\"3Q***********\\>\"F-7$ 7$F^fsF[zF^[t7$Fb[t7$F^fs$\"3;***********\\V\"F-7$7$F^fsF]tFd[t7$Fh[t7 $F^fs$\"3Q***********\\n\"F-7$7$F^fsFitFj[t7$F^\\t7$F^fs$\"3:********* **\\\">F-7$7$F^fsFeuF`\\t7$Fd\\t7$F^fs$\"3O***********\\:#F-7$7$F^fsFa vFf\\t7$Fj\\t7$F^fs$\"3c***********\\R#F-7$7$F^fsF^[lF\\]t7$F`]t7$F^fs $\"3z***********\\j#F-7$7$F^fsFi^lFb]t7$Ff]t7$F^fs$\"3+++++++vGF-7$7$F ^fsFfflFh]t7$F\\^t7$F^fs$\"3m++++++:JF-7$7$F^fsFbhnF^^t7$Fb^t7$F^fs$\" 3U++++++bLF-7$7$F^fsF[inFd^t7$Fh^t7$F^fs$\"33,+++++&f$F-7$7$F^fsFdinFj ^t7$F^_t7$F^fs$\"3&3+++++]$QF-7$7$F^fsF]jnF`_tF_jn-F$6U7$7$$!\"\"F*F(7 $Fi_t$!3t++++++?=F-7$7$Fi_tF7F[`t7$7$Fi_tFi^n7$Fi_t$!3u++++++!e\"F-7$7 $Fi_tFRFb`t7$7$Fi_tFbo7$Fi_t$!3u++++++S8F-7$7$Fi_tF`pFi`t7$F]at7$Fi_t$ !3u+++++++6F-7$7$Fi_tFgrF_at7$Fcat7$Fi_t$!3i2++++++')F_s7$7$Fi_tFgwFea t7$7$Fi_t$!3a,++++++!)F_s7$Fi_t$!3s2++++++iF_s7$7$Fi_tFg\\lF^bt7$Fbbt7 $Fi_t$!3!y++++++!QF_s7$7$Fi_tF_`lFdbt7$Fhbt7$Fi_t$!3!z++++++S\"F_s7$7$ Fi_tF`dlFjbt7$F^ct7$Fi_t$\"2+#**************F_s7$7$Fi_tF]elF`ct7$Fdct7 $Fi_t$\"3#>************R$F_s7$7$Fi_tFdalFfct7$Fjct7$Fi_t$\"3#=******** ****z&F_s7$7$Fi_tF`blF\\dt7$F`dt7$Fi_t$\"3u\"************>)F_s7$7$Fi_t F\\^lFbdt7$Ffdt7$Fi_t$\"3;************f5F-7$7$Fi_tF\\yFhdt7$F\\et7$Fi_ t$\"3;*************H\"F-7$7$Fi_tF[zF^et7$Fbet7$Fi_t$\"3:************R: F-7$7$Fi_tF]tFdet7$7$Fi_tF_en7$Fi_t$\"39************z?F-7$7$Fi_tFeuFaft7$Feft7$Fi_t$\"3!)*** *********fAF-7$7$Fi_tFavFgft7$F[gt7$Fi_t$\"3c*************\\#F-7$7$Fi_ tF^[lF]gt7$Fagt7$Fi_t$\"3x************RFF-7$7$Fi_tFi^lFcgt7$Fggt7$Fi_t $\"3)*************zHF-7$7$Fi_tFfflFigt7$F]ht7$Fi_t$\"3k++++++?KF-7$7$F i_tFbhnF_ht7$7$Fi_t$\"3e,+++++!G$F-7$Fi_t$\"3S++++++gMF-7$7$Fi_tF[inFh ht7$F\\it7$Fi_t$\"31,++++++PF-7$7$Fi_tFdinF^it7$7$Fi_t$\"3--+++++gPF-7 $Fi_t$\"3G,+++++SRF-7$7$Fi_tF]jnFgitF_jn-F$6U7$7$$!3++++++++vF_sF(7$F` jt$!3u++++++b>F-7$7$F`jtF7Fbjt7$7$F`jtF;7$F`jt$!3_++++++:++++++XGF-7$7$F`jtFfflF[bu 7$F_bu7$F`jt$\"3'************\\3$F-7$7$F`jtFbhnFabu7$Febu7$F`jt$\"3i++ ++++DLF-7$7$F`jtF[inFgbu7$F[cu7$F`jt$\"3%3+++++]c$F-7$7$F`jtFdinF]cu7$ Facu7$F`jt$\"30,+++++0QF-7$7$F`jtF]jnFccuF_jn-F$6U7$7$$\"3+++++++]7F-F (7$F\\du$!3T++++++N=F-7$7$F\\duF7F^du7$7$F\\duFi^n7$F\\du$!3U++++++&f \"F-7$7$F\\duFRFedu7$Fidu7$F\\du$!3U++++++b8F-7$7$F\\duF`pF[eu7$7$F\\d uFi_n7$F\\du$!3W++++++:6F-7$7$F\\duFgrFbeu7$Ffeu7$F\\du$!3W/+++++]()F_ s7$7$F\\duFgwFheu7$F\\fu7$F\\du$!3a/+++++]jF_s7$7$F\\duFg\\lF^fu7$Fbfu 7$F\\du$!3i/+++++]RF_s7$7$F\\duF_`lFdfu7$Fhfu7$F\\du$!3)\\++++++b\"F_s 7$7$F\\duF`dlFjfu7$F^gu7$F\\du$\"3m]***********\\)Fbdl7$7$F\\duF]elF`g u7$Fdgu7$F\\du$\"37&***********\\KF_s7$7$F\\duFdalFfgu7$Fjgu7$F\\du$\" 3-&***********\\cF_s7$7$F\\duF`blF\\hu7$F`hu7$F\\du$\"3#Q***********\\ !)F_s7$7$F\\duF\\^lFbhu7$Ffhu7$F\\du$\"3[***********\\/\"F-7$7$F\\duF \\yFhhu7$F\\iu7$F\\du$\"3[***********\\G\"F-7$7$F\\duF[zF^iu7$Fbiu7$F \\du$\"3Z***********\\_\"F-7$7$F\\duFd`oFdiu7$7$F\\duF]t7$F\\du$\"3C** *********\\w\"F-7$7$F\\duFitF[ju7$F_ju7$F\\du$\"3X***********\\+#F-7$7 $F\\duFeuFaju7$Feju7$F\\du$\"3m***********\\C#F-7$7$F\\duFavFgju7$F[[v 7$F\\du$\"3))***********\\[#F-7$7$F\\duF^[lF][v7$Fa[v7$F\\du$\"3`+++++ +DFF-7$7$F\\duFi^lFc[v7$Fg[v7$F\\du$\"3w++++++lHF-7$7$F\\duFfflFi[v7$7 $F\\du$\"3P,+++++SIF-7$F\\du$\"3'4+++++]?$F-7$7$F\\duFbhnFb\\v7$Ff\\v7 $F\\du$\"3t++++++XMF-7$7$F\\duF[inFh\\v7$F\\]v7$F\\du$\"3%4+++++]o$F-7 $7$F\\duFdinF^]v7$Fb]v7$F\\du$\"3g,+++++DRF-7$7$F\\duF]jnFd]vF_jn-F$6U 7$7$$\"3++++++++:F-F(7$F]^v$!3k++++++q>F-7$7$F]^vFi^nF_^v7$7$F]^vF77$F ]^v$!3l++++++IF-7$7$F_hvFeuFa^w7$Fe ^w7$F_hv$\"3a************HAF-7$7$F_hvFavFg^w7$F[_w7$F_hv$\"3w********* ***pCF-7$7$F_hvF^[lF]_w7$Fa_w7$F_hv$\"3'*************4FF-7$7$F_hvFi^lF c_w7$Fg_w7$F_hv$\"3=++++++]HF-7$7$F_hvFfflFi_w7$F]`w7$F_hv$\"3Q++++++! >$F-7$7$F_hvFbhnF_`w7$Fc`w7$F_hv$\"3g++++++IMF-7$7$F_hvF[inFe`w7$Fi`w7 $F_hv$\"3#3++++++n$F-7$7$F_hvFdinF[aw7$F_aw7$F_hv$\"3.,+++++5RF-7$7$F_ hvF]jnFaawF_jn-F$6U7$7$$\"3++++++++DF_sF(7$Fjaw$!3e++++++v promp t for each of the three questions below. Then change the formula to th e formulas listed below. Which of these relations appear to represent \+ the graph of a function?\n \011" }}{PARA 0 "" 0 "" {TEXT -1 153 " A. expr := 4*x^2 + 2*y^2 - y^3 = 1;\n \+ \011 B. expr := 4*x^2 + y^2 - y^3 = 1;\n\011 \+ C. expr := x^3 - x + 2*y^3 = 1;" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 89 "_________________________________________ ________________________________________________" }}{PARA 4 "" 0 "" {TEXT -1 23 "E. Horizontal Line Test" }}{PARA 0 "" 0 "" {TEXT -1 89 "_ ______________________________________________________________________ __________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 112 "Some functions have a sp ecial property where each x value has a unique y value not shared by a ny other x values." }}{PARA 0 "" 0 "" {TEXT -1 250 "These functions ar e called \"one-to-one\". When you look at the graph of a function, you can tell if its one-to-one if it passes the \"Horizontal Line Test\": If any horizontal line crosses the graph in two or more places, the f unction is not one-to-one." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "f := x -> x^3 - 3*x^2 + x -1;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6#%\"xG6\"6$%)operatorG%&arrowG F(,**$)9$\"\"$\"\"\"F1*&F0F1)F/\"\"#F1!\"\"F/F1F1F5F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 148 "plots[display]( plot( f(x), x= -2. .4, y=-7..7, color = blue, thickness=2),\n plot( \{seq( k/2, k = -10..10)\}, x= -2..4, y=-7..7, color =red));" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6:-%'CURVESG6%7S7$$!\"#\"\"!$!#BF*7 $$!3!******\\2<#p=!#<$!3So2C]F@))>!#;7$$!31++D^NUb.>y@fQ(F07$$!3*****\\7;)=,5F0$!3$eHSX3!* =,'F07$$!3M++]i83V()!#=$!3VR*HUH')e$[F07$$!3B******\\V'zV(FZ$!3Pq8(*z' ))\\\"QF07$$!3%)*****\\d;%)G'FZ$!3yjW2Wu$Q1$F07$$!3#*)*****\\!)H%*\\FZ $!3eP^hOIHsBF07$$!3Q+++]d'[p$FZ$!3\\cY8\"***[H=F07$$!3/******\\>iUCFZ$ !3TqM=>z#yV\"F07$$!3B++]7YY08FZ$!3e7]4>%)*Q=\"F07$$\"3%z-+++XDn%!#?$!3 qj;;5&GR&**FZ7$$\"3C++++y?#>\"FZ$!3IRQUtWD<#*FZ7$$\"3h****\\(3wY_#FZ$! 3Ly*z;8)fE#*FZ7$$\"3F)******HOTq$FZ$!3V.\"z/u?Q!**FZ7$$\"3I,+](3\">)* \\FZ$!3&e)e-NRxC6F07$$\"3_,+]isVIiFZ$!3!G\"yNV9l*H\"F07$$\"3&=++](o:;v FZ$!3_e1@(Qb&=:F07$$\"3#>++v$)[op)FZ$!3\"Q[^Ey#eTF07$$\"3&****\\(QIKH6F0$!3cix,@K[cAF07$$\"3#****\\7: xWC\"F0$!3eQSqG@MuCF07$$\"37++]Zn%)o8F0$!3O\">X5m7vo#F07$$\"3y******4F L(\\\"F0$!3'pMA[Bb;(GF07$$\"3#)****\\d6.B;F0$!3F5wzm;A/IF07$$\"3(**** \\(o3lW;1kRg\"GF07$$\" 3u***\\(=_(zC#F0$!3g&y))QB,Bb#F07$$\"3M+++b*=jP#F0$!3)*4/z3/aX@F07$$\" 3g***\\(3/3(\\#F0$!3WL`ED(H)Q;F07$$\"33++vB4JBEF0$!3scHm*pH(*o*FZ7$$\" 3u*****\\KCnu#F0$!3$GWaY;E6k\"FZ7$$\"3s***\\(=n#f(GF0$\"3#Hh_!fDA(\\)F Z7$$\"3P+++!)RO+IF0$\"3'e'o$\\fSO+#F07$$\"30++]_!>w7$F0$\"3]\\cqV())fP $F07$$\"3O++v)Q?QD$F0$\"3nw%\\6&\\5T\\F07$$\"3G+++5jypLF0$\"39NTdy)z)o lF07$$\"3<++]Ujp-NF0$\"3o(p\\MG=-n)F07$$\"3++++gEd@OF0$\"3m2@cA))Rx5F3 7$$\"39++v3'>$[PF0$\"3pR

N@E8F37$$\"37++D6EjpQF0$\"3c='R10c\"*e\"F37 $$\"\"%F*$\"#>F*-%'COLOURG6&%$RGBG$F*F*F_[l$\"*++++\"!\")-%*THICKNESSG 6#\"\"#-F$6$7S7$F($!\"&F*7$F.F[\\l7$F5F[\\l7$F:F[\\l7$F?F[\\l7$FDF[\\l 7$FIF[\\l7$FNF[\\l7$FSF[\\l7$FXF[\\l7$FhnF[\\l7$F]oF[\\l7$FboF[\\l7$Fg oF[\\l7$F\\pF[\\l7$FapF[\\l7$FfpF[\\l7$F\\qF[\\l7$FaqF[\\l7$FfqF[\\l7$ F[rF[\\l7$F`rF[\\l7$FerF[\\l7$FjrF[\\l7$F_sF[\\l7$FdsF[\\l7$FisF[\\l7$ F^tF[\\l7$FctF[\\l7$FhtF[\\l7$F]uF[\\l7$FbuF[\\l7$FguF[\\l7$F\\vF[\\l7 $FavF[\\l7$FfvF[\\l7$F[wF[\\l7$F`wF[\\l7$FewF[\\l7$FjwF[\\l7$F_xF[\\l7 $FdxF[\\l7$FixF[\\l7$F^yF[\\l7$FcyF[\\l7$FhyF[\\l7$F]zF[\\l7$FbzF[\\l7 $FgzF[\\l-F\\[l6&F^[lF`[lF_[lF_[l-F$6$7S7$F($!\"%F*7$F.Fc_l7$F5Fc_l7$F :Fc_l7$F?Fc_l7$FDFc_l7$FIFc_l7$FNFc_l7$FSFc_l7$FXFc_l7$FhnFc_l7$F]oFc_ l7$FboFc_l7$FgoFc_l7$F\\pFc_l7$FapFc_l7$FfpFc_l7$F\\qFc_l7$FaqFc_l7$Ff qFc_l7$F[rFc_l7$F`rFc_l7$FerFc_l7$FjrFc_l7$F_sFc_l7$FdsFc_l7$FisFc_l7$ F^tFc_l7$FctFc_l7$FhtFc_l7$F]uFc_l7$FbuFc_l7$FguFc_l7$F\\vFc_l7$FavFc_ l7$FfvFc_l7$F[wFc_l7$F`wFc_l7$FewFc_l7$FjwFc_l7$F_xFc_l7$FdxFc_l7$FixF c_l7$F^yFc_l7$FcyFc_l7$FhyFc_l7$F]zFc_l7$FbzFc_l7$FgzFc_lF]_l-F$6$7S7$ F($!\"$F*7$F.Fibl7$F5Fibl7$F:Fibl7$F?Fibl7$FDFibl7$FIFibl7$FNFibl7$FSF ibl7$FXFibl7$FhnFibl7$F]oFibl7$FboFibl7$FgoFibl7$F\\pFibl7$FapFibl7$Ff pFibl7$F\\qFibl7$FaqFibl7$FfqFibl7$F[rFibl7$F`rFibl7$FerFibl7$FjrFibl7 $F_sFibl7$FdsFibl7$FisFibl7$F^tFibl7$FctFibl7$FhtFibl7$F]uFibl7$FbuFib l7$FguFibl7$F\\vFibl7$FavFibl7$FfvFibl7$F[wFibl7$F`wFibl7$FewFibl7$Fjw Fibl7$F_xFibl7$FdxFibl7$FixFibl7$F^yFibl7$FcyFibl7$FhyFibl7$F]zFibl7$F bzFibl7$FgzFiblF]_l-F$6$7S7$F(F(7$F.F(7$F5F(7$F:F(7$F?F(7$FDF(7$FIF(7$ FNF(7$FSF(7$FXF(7$FhnF(7$F]oF(7$FboF(7$FgoF(7$F\\pF(7$FapF(7$FfpF(7$F \\qF(7$FaqF(7$FfqF(7$F[rF(7$F`rF(7$FerF(7$FjrF(7$F_sF(7$FdsF(7$FisF(7$ F^tF(7$FctF(7$FhtF(7$F]uF(7$FbuF(7$FguF(7$F\\vF(7$FavF(7$FfvF(7$F[wF(7 $F`wF(7$FewF(7$FjwF(7$F_xF(7$FdxF(7$FixF(7$F^yF(7$FcyF(7$FhyF(7$F]zF(7 $FbzF(7$FgzF(F]_l-F$6$7S7$F($!\"\"F*7$F.Fcil7$F5Fcil7$F:Fcil7$F?Fcil7$ FDFcil7$FIFcil7$FNFcil7$FSFcil7$FXFcil7$FhnFcil7$F]oFcil7$FboFcil7$Fgo Fcil7$F\\pFcil7$FapFcil7$FfpFcil7$F\\qFcil7$FaqFcil7$FfqFcil7$F[rFcil7 $F`rFcil7$FerFcil7$FjrFcil7$F_sFcil7$FdsFcil7$FisFcil7$F^tFcil7$FctFci l7$FhtFcil7$F]uFcil7$FbuFcil7$FguFcil7$F\\vFcil7$FavFcil7$FfvFcil7$F[w Fcil7$F`wFcil7$FewFcil7$FjwFcil7$F_xFcil7$FdxFcil7$FixFcil7$F^yFcil7$F cyFcil7$FhyFcil7$F]zFcil7$FbzFcil7$FgzFcilF]_l-F$6$7S7$F(F_[l7$F.F_[l7 $F5F_[l7$F:F_[l7$F?F_[l7$FDF_[l7$FIF_[l7$FNF_[l7$FSF_[l7$FXF_[l7$FhnF_ [l7$F]oF_[l7$FboF_[l7$FgoF_[l7$F\\pF_[l7$FapF_[l7$FfpF_[l7$F\\qF_[l7$F aqF_[l7$FfqF_[l7$F[rF_[l7$F`rF_[l7$FerF_[l7$FjrF_[l7$F_sF_[l7$FdsF_[l7 $FisF_[l7$F^tF_[l7$FctF_[l7$FhtF_[l7$F]uF_[l7$FbuF_[l7$FguF_[l7$F\\vF_ [l7$FavF_[l7$FfvF_[l7$F[wF_[l7$F`wF_[l7$FewF_[l7$FjwF_[l7$F_xF_[l7$Fdx F_[l7$FixF_[l7$F^yF_[l7$FcyF_[l7$FhyF_[l7$F]zF_[l7$FbzF_[l7$FgzF_[lF]_ l-F$6$7S7$F($\"\"\"F*7$F.F]`m7$F5F]`m7$F:F]`m7$F?F]`m7$FDF]`m7$FIF]`m7 $FNF]`m7$FSF]`m7$FXF]`m7$FhnF]`m7$F]oF]`m7$FboF]`m7$FgoF]`m7$F\\pF]`m7 $FapF]`m7$FfpF]`m7$F\\qF]`m7$FaqF]`m7$FfqF]`m7$F[rF]`m7$F`rF]`m7$FerF] `m7$FjrF]`m7$F_sF]`m7$FdsF]`m7$FisF]`m7$F^tF]`m7$FctF]`m7$FhtF]`m7$F]u F]`m7$FbuF]`m7$FguF]`m7$F\\vF]`m7$FavF]`m7$FfvF]`m7$F[wF]`m7$F`wF]`m7$ FewF]`m7$FjwF]`m7$F_xF]`m7$FdxF]`m7$FixF]`m7$F^yF]`m7$FcyF]`m7$FhyF]`m 7$F]zF]`m7$FbzF]`m7$FgzF]`mF]_l-F$6$7S7$F($Ff[lF*7$F.Fccm7$F5Fccm7$F:F ccm7$F?Fccm7$FDFccm7$FIFccm7$FNFccm7$FSFccm7$FXFccm7$FhnFccm7$F]oFccm7 $FboFccm7$FgoFccm7$F\\pFccm7$FapFccm7$FfpFccm7$F\\qFccm7$FaqFccm7$FfqF ccm7$F[rFccm7$F`rFccm7$FerFccm7$FjrFccm7$F_sFccm7$FdsFccm7$FisFccm7$F^ tFccm7$FctFccm7$FhtFccm7$F]uFccm7$FbuFccm7$FguFccm7$F\\vFccm7$FavFccm7 $FfvFccm7$F[wFccm7$F`wFccm7$FewFccm7$FjwFccm7$F_xFccm7$FdxFccm7$FixFcc m7$F^yFccm7$FcyFccm7$FhyFccm7$F]zFccm7$FbzFccm7$FgzFccmF]_l-F$6$7S7$F( $\"\"$F*7$F.Fhfm7$F5Fhfm7$F:Fhfm7$F?Fhfm7$FDFhfm7$FIFhfm7$FNFhfm7$FSFh fm7$FXFhfm7$FhnFhfm7$F]oFhfm7$FboFhfm7$FgoFhfm7$F\\pFhfm7$FapFhfm7$Ffp Fhfm7$F\\qFhfm7$FaqFhfm7$FfqFhfm7$F[rFhfm7$F`rFhfm7$FerFhfm7$FjrFhfm7$ F_sFhfm7$FdsFhfm7$FisFhfm7$F^tFhfm7$FctFhfm7$FhtFhfm7$F]uFhfm7$FbuFhfm 7$FguFhfm7$F\\vFhfm7$FavFhfm7$FfvFhfm7$F[wFhfm7$F`wFhfm7$FewFhfm7$FjwF hfm7$F_xFhfm7$FdxFhfm7$FixFhfm7$F^yFhfm7$FcyFhfm7$FhyFhfm7$F]zFhfm7$Fb zFhfm7$FgzFhfmF]_l-F$6$7S7$F(Fgz7$F.Fgz7$F5Fgz7$F:Fgz7$F?Fgz7$FDFgz7$F IFgz7$FNFgz7$FSFgz7$FXFgz7$FhnFgz7$F]oFgz7$FboFgz7$FgoFgz7$F\\pFgz7$Fa pFgz7$FfpFgz7$F\\qFgz7$FaqFgz7$FfqFgz7$F[rFgz7$F`rFgz7$FerFgz7$FjrFgz7 $F_sFgz7$FdsFgz7$FisFgz7$F^tFgz7$FctFgz7$FhtFgz7$F]uFgz7$FbuFgz7$FguFg z7$F\\vFgz7$FavFgz7$FfvFgz7$F[wFgz7$F`wFgz7$FewFgz7$FjwFgz7$F_xFgz7$Fd xFgz7$FixFgz7$F^yFgz7$FcyFgz7$FhyFgz7$F]zFgz7$FbzFgz7$FgzFgzF]_l-F$6$7 S7$F($\"\"&F*7$F.Fb]n7$F5Fb]n7$F:Fb]n7$F?Fb]n7$FDFb]n7$FIFb]n7$FNFb]n7 $FSFb]n7$FXFb]n7$FhnFb]n7$F]oFb]n7$FboFb]n7$FgoFb]n7$F\\pFb]n7$FapFb]n 7$FfpFb]n7$F\\qFb]n7$FaqFb]n7$FfqFb]n7$F[rFb]n7$F`rFb]n7$FerFb]n7$FjrF b]n7$F_sFb]n7$FdsFb]n7$FisFb]n7$F^tFb]n7$FctFb]n7$FhtFb]n7$F]uFb]n7$Fb uFb]n7$FguFb]n7$F\\vFb]n7$FavFb]n7$FfvFb]n7$F[wFb]n7$F`wFb]n7$FewFb]n7 $FjwFb]n7$F_xFb]n7$FdxFb]n7$FixFb]n7$F^yFb]n7$FcyFb]n7$FhyFb]n7$F]zFb] n7$FbzFb]n7$FgzFb]nF]_l-F$6$7S7$F($\"3++++++++]FZ7$F.Fh`n7$F5Fh`n7$F:F h`n7$F?Fh`n7$FDFh`n7$FIFh`n7$FNFh`n7$FSFh`n7$FXFh`n7$FhnFh`n7$F]oFh`n7 $FboFh`n7$FgoFh`n7$F\\pFh`n7$FapFh`n7$FfpFh`n7$F\\qFh`n7$FaqFh`n7$FfqF h`n7$F[rFh`n7$F`rFh`n7$FerFh`n7$FjrFh`n7$F_sFh`n7$FdsFh`n7$FisFh`n7$F^ tFh`n7$FctFh`n7$FhtFh`n7$F]uFh`n7$FbuFh`n7$FguFh`n7$F\\vFh`n7$FavFh`n7 $FfvFh`n7$F[wFh`n7$F`wFh`n7$FewFh`n7$FjwFh`n7$F_xFh`n7$FdxFh`n7$FixFh` n7$F^yFh`n7$FcyFh`n7$FhyFh`n7$F]zFh`n7$FbzFh`n7$FgzFh`nF]_l-F$6$7S7$F( $!3++++++++:F07$F.F^dn7$F5F^dn7$F:F^dn7$F?F^dn7$FDF^dn7$FIF^dn7$FNF^dn 7$FSF^dn7$FXF^dn7$FhnF^dn7$F]oF^dn7$FboF^dn7$FgoF^dn7$F\\pF^dn7$FapF^d n7$FfpF^dn7$F\\qF^dn7$FaqF^dn7$FfqF^dn7$F[rF^dn7$F`rF^dn7$FerF^dn7$Fjr F^dn7$F_sF^dn7$FdsF^dn7$FisF^dn7$F^tF^dn7$FctF^dn7$FhtF^dn7$F]uF^dn7$F buF^dn7$FguF^dn7$F\\vF^dn7$FavF^dn7$FfvF^dn7$F[wF^dn7$F`wF^dn7$FewF^dn 7$FjwF^dn7$F_xF^dn7$FdxF^dn7$FixF^dn7$F^yF^dn7$FcyF^dn7$FhyF^dn7$F]zF^ dn7$FbzF^dn7$FgzF^dnF]_l-F$6$7S7$F($\"3++++++++:F07$F.Fdgn7$F5Fdgn7$F: Fdgn7$F?Fdgn7$FDFdgn7$FIFdgn7$FNFdgn7$FSFdgn7$FXFdgn7$FhnFdgn7$F]oFdgn 7$FboFdgn7$FgoFdgn7$F\\pFdgn7$FapFdgn7$FfpFdgn7$F\\qFdgn7$FaqFdgn7$Ffq Fdgn7$F[rFdgn7$F`rFdgn7$FerFdgn7$FjrFdgn7$F_sFdgn7$FdsFdgn7$FisFdgn7$F ^tFdgn7$FctFdgn7$FhtFdgn7$F]uFdgn7$FbuFdgn7$FguFdgn7$F\\vFdgn7$FavFdgn 7$FfvFdgn7$F[wFdgn7$F`wFdgn7$FewFdgn7$FjwFdgn7$F_xFdgn7$FdxFdgn7$FixFd gn7$F^yFdgn7$FcyFdgn7$FhyFdgn7$F]zFdgn7$FbzFdgn7$FgzFdgnF]_l-F$6$7S7$F ($\"3++++++++DF07$F.Fjjn7$F5Fjjn7$F:Fjjn7$F?Fjjn7$FDFjjn7$FIFjjn7$FNFj jn7$FSFjjn7$FXFjjn7$FhnFjjn7$F]oFjjn7$FboFjjn7$FgoFjjn7$F\\pFjjn7$FapF jjn7$FfpFjjn7$F\\qFjjn7$FaqFjjn7$FfqFjjn7$F[rFjjn7$F`rFjjn7$FerFjjn7$F jrFjjn7$F_sFjjn7$FdsFjjn7$FisFjjn7$F^tFjjn7$FctFjjn7$FhtFjjn7$F]uFjjn7 $FbuFjjn7$FguFjjn7$F\\vFjjn7$FavFjjn7$FfvFjjn7$F[wFjjn7$F`wFjjn7$FewFj jn7$FjwFjjn7$F_xFjjn7$FdxFjjn7$FixFjjn7$F^yFjjn7$FcyFjjn7$FhyFjjn7$F]z Fjjn7$FbzFjjn7$FgzFjjnF]_l-F$6$7S7$F($\"3++++++++NF07$F.F`^o7$F5F`^o7$ F:F`^o7$F?F`^o7$FDF`^o7$FIF`^o7$FNF`^o7$FSF`^o7$FXF`^o7$FhnF`^o7$F]oF` ^o7$FboF`^o7$FgoF`^o7$F\\pF`^o7$FapF`^o7$FfpF`^o7$F\\qF`^o7$FaqF`^o7$F fqF`^o7$F[rF`^o7$F`rF`^o7$FerF`^o7$FjrF`^o7$F_sF`^o7$FdsF`^o7$FisF`^o7 $F^tF`^o7$FctF`^o7$FhtF`^o7$F]uF`^o7$FbuF`^o7$FguF`^o7$F\\vF`^o7$FavF` ^o7$FfvF`^o7$F[wF`^o7$F`wF`^o7$FewF`^o7$FjwF`^o7$F_xF`^o7$FdxF`^o7$Fix F`^o7$F^yF`^o7$FcyF`^o7$FhyF`^o7$F]zF`^o7$FbzF`^o7$FgzF`^oF]_l-F$6$7S7 $F($\"3++++++++XF07$F.Ffao7$F5Ffao7$F:Ffao7$F?Ffao7$FDFfao7$FIFfao7$FN Ffao7$FSFfao7$FXFfao7$FhnFfao7$F]oFfao7$FboFfao7$FgoFfao7$F\\pFfao7$Fa pFfao7$FfpFfao7$F\\qFfao7$FaqFfao7$FfqFfao7$F[rFfao7$F`rFfao7$FerFfao7 $FjrFfao7$F_sFfao7$FdsFfao7$FisFfao7$F^tFfao7$FctFfao7$FhtFfao7$F]uFfa o7$FbuFfao7$FguFfao7$F\\vFfao7$FavFfao7$FfvFfao7$F[wFfao7$F`wFfao7$Few Ffao7$FjwFfao7$F_xFfao7$FdxFfao7$FixFfao7$F^yFfao7$FcyFfao7$FhyFfao7$F ]zFfao7$FbzFfao7$FgzFfaoF]_l-F$6$7S7$F($!3++++++++XF07$F.F\\eo7$F5F\\e o7$F:F\\eo7$F?F\\eo7$FDF\\eo7$FIF\\eo7$FNF\\eo7$FSF\\eo7$FXF\\eo7$FhnF \\eo7$F]oF\\eo7$FboF\\eo7$FgoF\\eo7$F\\pF\\eo7$FapF\\eo7$FfpF\\eo7$F\\ qF\\eo7$FaqF\\eo7$FfqF\\eo7$F[rF\\eo7$F`rF\\eo7$FerF\\eo7$FjrF\\eo7$F_ sF\\eo7$FdsF\\eo7$FisF\\eo7$F^tF\\eo7$FctF\\eo7$FhtF\\eo7$F]uF\\eo7$Fb uF\\eo7$FguF\\eo7$F\\vF\\eo7$FavF\\eo7$FfvF\\eo7$F[wF\\eo7$F`wF\\eo7$F ewF\\eo7$FjwF\\eo7$F_xF\\eo7$FdxF\\eo7$FixF\\eo7$F^yF\\eo7$FcyF\\eo7$F hyF\\eo7$F]zF\\eo7$FbzF\\eo7$FgzF\\eoF]_l-F$6$7S7$F($!3++++++++NF07$F. Fbho7$F5Fbho7$F:Fbho7$F?Fbho7$FDFbho7$FIFbho7$FNFbho7$FSFbho7$FXFbho7$ FhnFbho7$F]oFbho7$FboFbho7$FgoFbho7$F\\pFbho7$FapFbho7$FfpFbho7$F\\qFb ho7$FaqFbho7$FfqFbho7$F[rFbho7$F`rFbho7$FerFbho7$FjrFbho7$F_sFbho7$Fds Fbho7$FisFbho7$F^tFbho7$FctFbho7$FhtFbho7$F]uFbho7$FbuFbho7$FguFbho7$F \\vFbho7$FavFbho7$FfvFbho7$F[wFbho7$F`wFbho7$FewFbho7$FjwFbho7$F_xFbho 7$FdxFbho7$FixFbho7$F^yFbho7$FcyFbho7$FhyFbho7$F]zFbho7$FbzFbho7$FgzFb hoF]_l-F$6$7S7$F($!3++++++++DF07$F.Fh[p7$F5Fh[p7$F:Fh[p7$F?Fh[p7$FDFh[ p7$FIFh[p7$FNFh[p7$FSFh[p7$FXFh[p7$FhnFh[p7$F]oFh[p7$FboFh[p7$FgoFh[p7 $F\\pFh[p7$FapFh[p7$FfpFh[p7$F\\qFh[p7$FaqFh[p7$FfqFh[p7$F[rFh[p7$F`rF h[p7$FerFh[p7$FjrFh[p7$F_sFh[p7$FdsFh[p7$FisFh[p7$F^tFh[p7$FctFh[p7$Fh tFh[p7$F]uFh[p7$FbuFh[p7$FguFh[p7$F\\vFh[p7$FavFh[p7$FfvFh[p7$F[wFh[p7 $F`wFh[p7$FewFh[p7$FjwFh[p7$F_xFh[p7$FdxFh[p7$FixFh[p7$F^yFh[p7$FcyFh[ p7$FhyFh[p7$F]zFh[p7$FbzFh[p7$FgzFh[pF]_l-F$6$7S7$F($!3++++++++]FZ7$F. F^_p7$F5F^_p7$F:F^_p7$F?F^_p7$FDF^_p7$FIF^_p7$FNF^_p7$FSF^_p7$FXF^_p7$ FhnF^_p7$F]oF^_p7$FboF^_p7$FgoF^_p7$F\\pF^_p7$FapF^_p7$FfpF^_p7$F\\qF^ _p7$FaqF^_p7$FfqF^_p7$F[rF^_p7$F`rF^_p7$FerF^_p7$FjrF^_p7$F_sF^_p7$Fds F^_p7$FisF^_p7$F^tF^_p7$FctF^_p7$FhtF^_p7$F]uF^_p7$FbuF^_p7$FguF^_p7$F \\vF^_p7$FavF^_p7$FfvF^_p7$F[wF^_p7$F`wF^_p7$FewF^_p7$FjwF^_p7$F_xF^_p 7$FdxF^_p7$FixF^_p7$F^yF^_p7$FcyF^_p7$FhyF^_p7$F]zF^_p7$FbzF^_p7$FgzF^ _pF]_l-%+AXESLABELSG6$Q\"x6\"Q\"yFdbp-%%VIEWG6$;F(Fgz;$!\"(F*$\"\"(F* " 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "C urve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "C urve 9" "Curve 10" "Curve 11" "Curve 12" "Curve 13" "Curve 14" "Curve \+ 15" "Curve 16" "Curve 17" "Curve 18" "Curve 19" "Curve 20" "Curve 21" "Curve 22" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 122 "Although this is the graph of a function, its not one-to-one b ecause various horizontal lines cross the graph in 3 places!" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 237 "E1. Highlight and c opy the block of code above, then paste it at a new > prompt for each \+ of the three questions below. Change each function to the function lis ted below. Which of these functions appear to be the one-to-one functi ons?\n " }}{PARA 0 "" 0 "" {TEXT -1 172 " A. f(x) = xsin(x)\011 \+ B. f(x) = 1/(x+1)\011 \+ \011C. f(x) =-2-x \+ D. f(x) = x|x|" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "3 0" 1 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }