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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 38 "More Concerning Functio
ns and Graphing" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;
" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 20 "More about Functions" }}
{SECT 1 {PARA 4 "" 0 "" {TEXT -1 15 "Function Basics" }}{PARA 0 "" 0 "
" {TEXT -1 23 "Recall that we use the " }{TEXT 264 2 "->" }{TEXT -1 
91 " (minus greater than) notation to define a function. Suppose we wa
nt to enter the function " }{XPPEDIT 18 0 "f(x) = x^4+x^3;" "6#/-%\"fG
6#%\"xG,&*$F'\"\"%\"\"\"*$F'\"\"$F+" }{TEXT -1 102 " . Suppose, by acc
ident, we forget to enter this as function but instead enter this as a
n expression. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "f := x^4+x
^3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,&*$)%\"xG\"\"%\"\"\"F**$
)F(\"\"$F*F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 65 "Note, since this \+
is an expression, we cannot find f(3) properly. " }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 5 "f(3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)
-%\"xG6#\"\"$\"\"%\"\"\"F+*$)F&F)F+F+" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 79 "We could simply fix this by reentering the expression as \+
a function or use the " }{TEXT 265 7 "unapply" }{TEXT -1 14 " command.
 The " }{TEXT 266 8 "unapply " }{TEXT -1 21 "command has the form " }
{TEXT 267 7 "unapply" }{TEXT -1 1 "(" }{TEXT 268 21 "expression, varia
ble)" }{TEXT -1 7 ", were " }{TEXT 269 10 "expression" }{TEXT -1 45 " \+
is converted to a function of the specified " }{TEXT 270 8 "variable" 
}{TEXT -1 73 ". To convert the expression f stored above to function o
f x, we can enter" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f := u
napply(f, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%
)operatorG%&arrowGF(,&*$)9$\"\"%\"\"\"F1*$)F/\"\"$F1F1F(F(F(" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 109 "Having f now expressed as a funct
ion now allows us to easily do many different types of function evalua
tions." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "f(3);  simplify(f
(x-2));  simplify((f(x+h)-f(x))/h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#\"$3\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*$)%\"xG\"\"%\"\"\"F(*&\"
\"(F()F&\"\"$F(!\"\"*&\"#=F()F&\"\"#F(F(*&\"#?F(F&F(F-\"\")F(" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,0*&\"\"%\"\"\")%\"xG\"\"$F&F&*(\"\"'F
&)F(\"\"#F&%\"hGF&F&*(F%F&F(F&)F.F-F&F&*$)F.F)F&F&*&F)F&F,F&F&*(F)F&F(
F&F.F&F&*$F0F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "Recall, to un
assign f , we can enter" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "f
 := 'f';" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGF$" }}}}{SECT 1 
{PARA 4 "" 0 "" {TEXT -1 11 "Composition" }}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 64 "Maple makes it easy to define the composition of function
s. Let " }{XPPEDIT 18 0 "f(x) = sqrt(x+1);" "6#/-%\"fG6#%\"xG-%%sqrtG6
#,&F'\"\"\"F,F," }{TEXT -1 5 " and " }{XPPEDIT 18 0 "g(x) = x^2-4*x+5;
" "6#/-%\"gG6#%\"xG,(*$F'\"\"#\"\"\"*&\"\"%F+F'F+!\"\"\"\"&F+" }{TEXT 
-1 58 ". We enter these functions and form f(g(x)) and g(f(x)).  " }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "f := x->sqrt(x+1); g := x ->
 x^2-4*x+5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)o
peratorG%&arrowGF(-%%sqrtG6#,&9$\"\"\"F1F1F(F(F(" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"gGf*6#%\"xG6\"6$%)operatorG%&arrowGF(,(*$)9$\"\"#\"
\"\"F1*&\"\"%F1F/F1!\"\"\"\"&F1F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 28 "Now compute the compositions" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 17 "f(g(x)); g(f(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#*$,(*$)%\"xG\"\"#\"\"\"F)*&\"\"%F)F'F)!\"\"\"\"'F)#F)F(" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#,(%\"xG\"\"\"\"\"'F%*&\"\"%F%,&F$F%F%F%#F%\"\"#
!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 8 "Graphing" }}
{EXCHG {PARA 0 "" 0 "" {TEXT 275 50 "The command that graphs functions
 in Maple is the " }{TEXT 271 4 "plot" }{TEXT 276 14 " command. The " 
}{TEXT 272 4 "plot" }{TEXT 277 28 " command has the structure  " }
{TEXT 273 4 "plot" }{TEXT 278 1 "(" }{TEXT -1 40 "expression or functi
on , range , options" }{TEXT 274 31 "), where expression or function" 
}{TEXT -1 48 " is the expression or function we want to play, " }
{TEXT 279 5 "range" }{TEXT -1 75 " gives the interval on the x-axis fo
r which the graph will be plotted, and " }{TEXT 280 7 "options" }
{TEXT -1 155 " are specfied parameters that are given to add to the gr
aph in a certain way (more details on this will be given below).\nTo d
o simple plot of the function " }{XPPEDIT 18 0 "f(x) = x^2-4*x+3;" "6#
/-%\"fG6#%\"xG,(*$)F'\"\"#\"\"\"F,*&\"\"%F,F'F,!\"\"\"\"$F," }{TEXT 
-1 15 ",  we can enter" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "f
 := x^2-4*x+3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,(*$)%\"xG\"\"
#\"\"\"F**&\"\"%F*F(F*!\"\"\"\"$F*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "plot(f, x = -2..5);" }}{PARA 13 "" 1 "" {GLPLOT2D 
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PVt(*!#>$\"3mjls]$*[+MF07$$\"3([,++Dxg$[Fio$\"3K'z;Vn&*)3GF07$$\"3^nmT
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D[l(FP$\"3jK'))3*GLS_FP7$$\"3u.+voibk\"*FP$\"3t$[3`3%oS<FP7$$\"3a+]i!o
<-1\"F0$!31k9!>#>4o6FP7$$\"3qLL3-$=-@\"F0$!3iv'ejp[Cw$FP7$$\"3kL$3xplz
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78Z!z%[F0$\"3!=fR]Dh06(F07$$\"\"&F*$\"\")F*-%'COLOURG6&%$RGBG$\"#5!\"
\"$F*F*Fb[l-%+AXESLABELSG6$Q\"x6\"Q!Fg[l-%%VIEWG6$;F(Fgz%(DEFAULTG" 1 
2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 135 "In the preceding command, the fun
ction in the first parameter was entered as an expression.  To plot as
 a function, we could also enter" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 19 "f := x-> x^2-4*x+3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arrowGF(,(*$)9$\"\"#\"\"\"F1*&\"\"%
F1F/F1!\"\"\"\"$F1F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 
"plot(f(x), x = -2..5);" }}{PARA 13 "" 1 "" {GLPLOT2D 486 486 486 
{PLOTDATA 2 "6%-%'CURVESG6$7S7$$!\"#\"\"!$\"#:F*7$$!3GLL$3#*>u%=!#<$\"
3;<Ds/SE!Q\"!#;7$$!3om;z43m9<F0$\"3;3-=$\\q)z7F37$$!3QLLe/$f`c\"F0$\"3
1&*y2(py6<\"F37$$!3PLL3K\"o]T\"F0$\"3%[6xY.pi1\"F37$$!3]m;Hn7\\l7F0$\"
3[M\"en@LMm*F07$$!3WL$ekO9o7\"F0$\"33G-H#3opx)F07$$!3:***\\7oCA$)*!#=$
\"37;eK%H;'**yF07$$!3qJLe9_>Z$)FP$\"3vhpLlZjNqF07$$!3-++Dc#Gp'oFP$\"3X
Y[ER$=$=iF07$$!3lkmmT<HW`FP$\"3`Jr')Q7LBaF07$$!3/KL$3n_J+%FP$\"3qLLR\"
Q8:w%F07$$!3!p****\\sZL\\#FP$\"3QDwx=p]fSF07$$!3]$*****\\PVt(*!#>$\"3m
jls]$*[+MF07$$\"3([,++Dxg$[Fio$\"3K'z;Vn&*)3GF07$$\"3^nmT&G\"H5=FP$\"3
F))Q@J]l3BF07$$\"39NLLej%yQ$FP$\"3U!RVh[O'f<F07$$\"3gOLLLCCCZFP$\"3;Qd
N#p([L8F07$$\"3-,+vo()yyiFP$\"3`7\"e_wjr#))FP7$$\"3!GLLLoD[l(FP$\"3jK'
))3*GLS_FP7$$\"3u.+voibk\"*FP$\"3t$[3`3%oS<FP7$$\"3a+]i!o<-1\"F0$!31k9
!>#>4o6FP7$$\"3qLL3-$=-@\"F0$!3iv'ejp[Cw$FP7$$\"3kL$3xplzM\"F0$!3'y>]j
o7&[dFP7$$\"3gmm\"H([a'\\\"F0$!3'f/N,NH`Y(FP7$$\"3wm;ayo(3l\"F0$!3s+>j
g/8\"y)FP7$$\"3?+]7VLA&y\"F0$!3-&)fhw)4(Q&*FP7$$\"3'pm;a?@.$>F0$!3=QT&
el[9&**FP7$$\"3)******\\\\@-3#F0$!3%=l*R<^kN**FP7$$\"3Q++v$opoA#F0$!3#
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6jOXeA#FP7$$\"3;L$3-\"QfYKF0$\"3'\\I(\\w7'*RbFP7$$\"3C+]PWF'QR$F0$\"31
sgc,N`G%*FP7$$\"3[LL$e/Xy`$F0$\"3GFT*\\Qn\\O\"F07$$\"3m**\\(=<\"e)o$F0
$\"3%pu5SP18&=F07$$\"3%ymmm(zvLQF0$\"3+K'))pJoEO#F07$$\"3-nm\"zAAA)RF0
$\"3G:p%3'\\?HHF07$$\"3LM$3-7d%HTF0$\"3gsf!oi(eMNF07$$\"3#4++]p]ZE%F0$
\"3_()H]5d4HTF07$$\"3$QL$e*R7)>WF0$\"3k]s<\\?\\b[F07$$\"3'pmmmV,&eXF0$
\"3Q*RD9gHfa&F07$$\"3<+](o(GP1ZF0$\"3rlYo[TXCjF07$$\"3g+]78Z!z%[F0$\"3
!=fR]Dh06(F07$$\"\"&F*$\"\")F*-%'COLOURG6&%$RGBG$\"#5!\"\"$F*F*Fb[l-%+
AXESLABELSG6$Q\"x6\"Q!Fg[l-%%VIEWG6$;F(Fgz%(DEFAULTG" 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 "" {TEXT -1 193 "To graph the function in certain ways, we can ad
d more parameters involving options. Here are a few of the options ava
ilable. These and other options can be see by specifying ? plot[option
s].\n\n" }{TEXT 281 24 "view( x-range, y-range) " }{TEXT -1 93 "    le
ts you select the viewing rectangle, like the windows command on a gra
phing calculator\n" }{TEXT 282 9 "thickness" }{TEXT -1 146 "          \+
                 the thickness of the curve (values can be 1, 2, or 3 \+
- default is 1), useful if curve is barely visible in a printout.\n" }
{TEXT 283 5 "color" }{TEXT -1 108 "                                  c
olor of the curve. If not specified, a default color is chosen by Mapl
e.\n" }{TEXT 284 5 "title" }{TEXT -1 77 "                             \+
       title (specified in quotes) of the graph\n" }{TEXT 285 9 "numpo
ints" }{TEXT -1 351 "                         selecting a large number
 will increase the resolution of the graph and take out artificial cor
ners\n\nIf you click on the graph you'll see some additional icons at \+
the top of the screen, which may help to improve the looks of your gra
ph. For the previous function, we can add some these options and the n
ext command illustrates:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 99 
"plot(f(x), x = -1 .. 5, view = [-2..5, -2..6], thickness = 3, color =
 blue, title = \"my parabola\");" }}{PARA 13 "" 1 "" {GLPLOT2D 486 
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{PARA 0 "" 0 "" {TEXT -1 49 "In the previous command, we plotted the f
unction " }{XPPEDIT 18 0 "f(x) = x^2-4*x+3;" "6#/-%\"fG6#%\"xG,(*$F'\"
\"#\"\"\"*&\"\"%F+F'F+!\"\"\"\"$F+" }{TEXT -1 40 " with points specfie
d over the interval " }{TEXT 286 1 "x" }{TEXT -1 33 " = -1..5. To view
 the graph, the " }{TEXT 287 1 "x" }{TEXT -1 34 " axis ranges from -2 \+
to 5 and the " }{TEXT 288 1 "y" }{TEXT -1 166 " axis ranges from -2 to
 6. The thickness option of 3 gives the graph maximum resolution. The \+
color of the graph is specified to be blue with a title of \"my parabo
la\"." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 228 "There are a couple of m
ethods available for graphing multiple curves on the same graph. One m
ethod encloses the functions to be plotted within brackets separated b
y commas. To demonstrate, suppose we desire to plot the function " }
{XPPEDIT 18 0 "f(x) = cos(Pi*x/2);" "6#/-%\"fG6#%\"xG-%$cosG6#*(%#PiG
\"\"\"F'F-\"\"#!\"\"" }{TEXT -1 42 " in red with a thickness of 2, alo
ng with " }{XPPEDIT 18 0 "g(x) = e^(-x)" "6#/-%\"gG6#%\"xG)%\"eG,$F'!
\"\"" }{TEXT -1 73 "  in blue with a thickness of 1. We plot these fun
ctions on the interval " }{XPPEDIT 18 0 "[-Pi, 3*Pi];" "6#7$,$%#PiG!\"
\"*&\"\"$\"\"\"F%F)" }{TEXT -1 49 ". The following commands accomplish
es this task.\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "f := x -
> cos(1/2*Pi*x); g := x -> exp(-x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arrowGF(-%$cosG6#,$*&#\"\"\"\"\"#F2*
&%#PiGF29$F2F2F2F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGf*6#%
\"xG6\"6$%)operatorG%&arrowGF(-%$expG6#,$9$!\"\"F(F(F(" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "plot([f(x), g(x)], x = -Pi .. 3*Pi,
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1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 294 "Another method for plotting the graph involves
 storing each separate graph plots as variables and displaying them to
gether. This feature especially convenient when one wants to graph fun
ctions over different intervals on the x axis. To demonstrate, suppose
 we enter the following two functions:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 32 "f := x -> x^2; 1; g := x -> x^5;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arrowGF(*$)9$\"\"#\"\"
\"F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"gGf*6#%\"xG6\"6$%)operatorG%&arrowGF(*$)9$\"\"&\"
\"\"F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 97 "The following comma
nds set up and store the plots for these graphs in the variables p1 an
d p2. \n\n" }{TEXT 291 6 "NOTE!!" }{TEXT -1 180 " An important fact to
 remember is to end thesecommands with a colon : . If you end the comm
and with a semicolon, all the data points generated to plot the graph \+
will be displayed.\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "p1 \+
:= plot(f(x), x = -3 .. 3, color = blue):" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 64 "p2 := plot(g(x), x = -1.2 .. 1.2, color = black, th
ickness = 2):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 124 "Note the differ
ent interval values for x that are specified. To plot the two graphs, \+
we must specify a command in the Maple " }{TEXT 292 5 "plots" }{TEXT 
-1 14 " package. The " }{TEXT 293 5 "plots" }{TEXT -1 120 " package is
 not available as a standard part of Maple and must be read in. This c
an be done with the following statement" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "with(plots);" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning,
 the name changecoords has been redefined\n" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#7gn%,InteractiveG%(animateG%*animate3dG%-animatecurveG%
&arrowG%-changecoordsG%,complexplotG%.complexplot3dG%*conformalG%,conf
ormal3dG%,contourplotG%.contourplot3dG%*coordplotG%,coordplot3dG%-cyli
nderplotG%,densityplotG%(displayG%*display3dG%*fieldplotG%,fieldplot3d
G%)gradplotG%+gradplot3dG%,graphplot3dG%-implicitplotG%/implicitplot3d
G%(inequalG%,interactiveG%2interactiveparamsG%-listcontplotG%/listcont
plot3dG%0listdensityplotG%)listplotG%+listplot3dG%+loglogplotG%(logplo
tG%+matrixplotG%)multipleG%(odeplotG%'paretoG%,plotcompareG%*pointplot
G%,pointplot3dG%*polarplotG%,polygonplotG%.polygonplot3dG%4polyhedra_s
upportedG%.polyhedraplotG%'replotG%*rootlocusG%,semilogplotG%+setoptio
nsG%-setoptions3dG%+spacecurveG%1sparsematrixplotG%+sphereplotG%)surfd
ataG%)textplotG%+textplot3dG%)tubeplotG" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 123 "The output of the preceding statement gives all the new \+
commands that we now have available to use. The one we need is the " }
{TEXT 296 7 "display" }{TEXT -1 42 " command. To display the plots sto
red in  " }{TEXT 294 3 "p1 " }{TEXT -1 4 "and " }{TEXT 295 2 "p2" }
{TEXT -1 10 ", we enter" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 
"display([p1, p2], view = [-4 .. 4, -5 .. 10], title = \"f(x) = x^2 an
d g(x) = x^5 with different intervals\");" }}{PARA 13 "" 1 "" 
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\"#5F*" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve
 1" "Curve 2" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "Note in the prec
eding " }{TEXT 297 7 "display" }{TEXT -1 92 " command that the same op
tions, such as view and title, can be specified like we did in the " }
{TEXT 298 4 "plot" }{TEXT -1 9 " command." }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "Exercises
" }}{PARA 0 "" 0 "" {TEXT -1 79 "1. Using the unapply command, convert
 the assignment to a function and compute " }{XPPEDIT 18 0 "f(3*Pi/4);
" "6#-%\"fG6#*(\"\"$\"\"\"%#PiGF(\"\"%!\"\"" }{TEXT -1 29 ".          \+
                  " }}{PARA 0 "" 0 "" {TEXT -1 24 ">  f := tan(x) + se
c(x);" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 71 "
2.  Determine f(g(x)) and g(f(x)) for the following functions.\n     a
. " }{XPPEDIT 18 0 "f(x) = x^3+x^2+1;" "6#/-%\"fG6#%\"xG,(*$)F'\"\"$\"
\"\"F,*$)F'\"\"#F,F,F,F," }{TEXT -1 5 " and " }{XPPEDIT 18 0 "g(x) = 2
*x^4+x;" "6#/-%\"gG6#%\"xG,&*&\"\"#\"\"\"*$)F'\"\"%F+F+F+F'F+" }{TEXT 
-1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 8 "     b. " }{XPPEDIT 18 0 "f(x) \+
= arcsin(x^2);" "6#/-%\"fG6#%\"xG-%'arcsinG6#*$)%\"xG\"\"#\"\"\"" }
{TEXT -1 7 " and   " }{XPPEDIT 18 0 "g(x) = sqrt(sin(x));" "6#/-%\"gG6
#%\"xG-%%sqrtG6#-%$sinG6#F'" }{TEXT -1 28 "                           \+
 " }}{PARA 0 "" 0 "" {TEXT -1 20 "     \n3.  Using the " }{TEXT 299 5 
"plot " }{TEXT -1 47 "command, graph the following functions\n     a. \+
" }{XPPEDIT 18 0 "f(x) = x^2-2*x-3;" "6#/-%\"fG6#%\"xG,(*$)F'\"\"#\"\"
\"F,*&F+F,F'F,!\"\"\"\"$F." }{TEXT -1 9 "\n     b. " }{XPPEDIT 18 0 "g
(x) = e^sin(x);" "6#/-%\"gG6#%\"xG)%\"eG-%$sinG6#F'" }{TEXT -1 48 ". N
ote this function can be created by entering " }{TEXT 300 20 "g := x->
exp(sin(x));" }{TEXT -1 16 "\n\n4.  Using the " }{TEXT 301 4 "plot" }
{TEXT -1 189 " command, plot the following functions on the same graph
. Color one function red with a thickness of 2 and\n     the other blu
e with a thickness of 1. Create a title for your graph.\n     a. " }
{XPPEDIT 18 0 "f(x) = x^2;" "6#/-%\"fG6#%\"xG*$)F'\"\"#\"\"\"" }{TEXT 
-1 5 " and " }{XPPEDIT 18 0 "g(x) = x^3;" "6#/-%\"gG6#%\"xG*$)F'\"\"$
\"\"\"" }{TEXT -1 43 " .                               .\n     b. " }
{XPPEDIT 18 0 "f(x) = ln(x^2);" "6#/-%\"fG6#%\"xG-%#lnG6#*$)F'\"\"#\"
\"\"" }{TEXT -1 5 " and " }{XPPEDIT 18 0 "g(x) = e^sin(x);" "6#/-%\"gG
6#%\"xG)%\"eG-%$sinG6#F'" }{TEXT -1 104 ".                         .\n
5.   By storing your plots and using the display command, plot the gra
ph of " }{XPPEDIT 18 0 "f(x) = e^(x^2);" "6#/-%\"fG6#%\"xG)%\"eG*$)F'
\"\"#\"\"\"" }{TEXT -1 0 "" }{TEXT -1 56 "  on the interval -2 <= x <=
 2 and the \n      graph of  " }{XPPEDIT 18 0 "f(x) = sin(x^2);" "6#/-
%\"fG6#%\"xG-%$sinG6#*$)F'\"\"#\"\"\"" }{TEXT -1 20 "  on the interval
   " }{XPPEDIT 18 0 "-2*Pi;" "6#,$*&\"\"#\"\"\"%#PiGF&!\"\"" }{TEXT 
-1 9 " <= x <= " }{XPPEDIT 18 0 "2*Pi;" "6#*&\"\"#\"\"\"%#PiGF%" }
{TEXT -1 3 " .\n" }}}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 
1 }{PAGENUMBERS 0 1 2 33 1 1 }