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{SECT 0 {PARA 4 "" 0 "" {TEXT -1 18 "Module 1 : Algebra" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 3 "" 0 "" {TEXT -1 33 "105 : Graphs - Seein
g & Believing" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 259 "" 0 "" {TEXT -1 17 "O B J E C T I V E" }}
{PARA 0 "" 0 "" {TEXT -1 402 "The objective of this module is to learn
 to create graphs in Maple, learn some of the options which can make g
raphs more interesting and informative, and how to create graphs of mu
ltiple functions at once. We will also learn about lines and slope, an
d how parameters in a function can affect the placement of the graph, \+
that will be helpful later when you need to graph on your own without \+
using Maple." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" 
{TEXT -1 9 "S E T U P" }}{PARA 0 "" 0 "" {TEXT -1 253 "In this project
 we will use the following command packages. Type and execute this lin
e before beginning the project below. If you re-enter the worksheet fo
r this project, be sure to re-execute this statement before jumping to
 any point in the worksheet." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart; with(p
lots):" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 83 "_____
______________________________________________________________________
________" }}{PARA 4 "" 0 "" {TEXT -1 15 "A. Basic Graphs" }}{PARA 0 "
" 0 "" {TEXT -1 83 "__________________________________________________
_________________________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 215 "The plot
 command will graph a function.You must specify a function (no y, just
 a formula in x) and a domain (the range of values to use for  x). Map
le will automatically compute the range (y range) to fit the graph." }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 19 "plot(x^2, x=-3..3);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 
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{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 51 "You can also define a fun
ction first, then plot it." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG 
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/7$$\"39++v3'>$[FF/$\"3_Y-;G$RnW\"F/7$$\"37++D6EjpGF/$\"3?d]]kn3_wF27$
$\"\"$F*F+-%'COLOURG6&%$RGBG$\"#5!\"\"F+F+-%+AXESLABELSG6$Q\"x6\"Q!6\"
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45.000000 0 0 "Curve 1" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 49 "A1. Graph y = 2x +
 3 using a domain of x = -5..5\n" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 60 "A2. Graph
 the following using domains of your own choice\n\011A." }{XPPEDIT 19 
1 "4-(x-3)^2;" "6#,&\"\"%\"\"\"*$,&%\"xGF%\"\"$!\"\"\"\"#F*" }{TEXT 
-1 52 "           B.   sqrt ( x- 1)                     C. " }
{XPPEDIT 19 1 "x^3-12*x^2+30*x-10;" "6#,**$%\"xG\"\"$\"\"\"*&\"#7F'*$F
%\"\"#F'!\"\"*&\"#IF'F%F'F'\"#5F," }{TEXT -1 21 " (Domain = [-4,11])  \+
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 36 "A3. A. De
fine the function f(x)  =  " }{XPPEDIT 19 1 "25*x+8*x^2-x^3;" "6#,(*&
\"#D\"\"\"%\"xGF&F&*&\"\")F&*$F'\"\"#F&F&*$F'\"\"$!\"\"" }{TEXT -1 
347 "\n      B. Experiment with different domains until you can create
 a graph with the smallest domain that shows all three of this functio
ns x intercepts. Hint start with x = -20..20,                     then
 shorten the interval on both sides using integer values until you can
't shorten the interval any more without losing sight of an x-intercep
t. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 83 "________
______________________________________________________________________
_____" }}{PARA 4 "" 0 "" {TEXT -1 19 "B. Graphing Options" }}{PARA 0 "
" 0 "" {TEXT -1 83 "__________________________________________________
_________________________________" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 104 "There ar
e a number of options which can be used to enhance your graphs and mak
e them more sophisticated." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
257 "" 0 "" {TEXT -1 17 "STYLISTIC OPTIONS" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 159 "There are a number of options \+
which can be used to enhance your graphs. These options can be supplie
d in any order after the domain (and range) are specified. " }}{PARA 
3 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT 256 14 "Line Thickness" }{TEXT -1 156 "\nThe default thickn
ess is 1 which sometimes results in a graph that is somewhat thin and \+
hard to see for lighter colors. Larger numbers make thicker graphs." }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 18 "Color o
f the Curve" }{TEXT -1 280 "\nMaple chooses colors for the graph on it
s own unless we specify a color. The 25 colors available are aquamarin
e, black, blue, navy, coral, cyan, brown, gold, green, gray, grey, kha
ki, magenta, maroon, orange, pink, plum, red, sienna, tan, turquoise, \+
violet, wheat, white, yellow " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT 258 10 "Line Style" }{TEXT -1 141 "\nLine styles
 create dashed and dotted graphs. The default value is 1 if you dont s
pecify a linestyle and  creates a standard connected graph." }}{PARA 
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{PARA 257 "" 0 "" {TEXT -1 14 "VERTICAL RANGE" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 123 "Maple computes the range
 of y values to use in a graph automatically. However sometimes the re
sults are not what we expect." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 129 "The problem here is that the values of t
he function get very large near x = 1 and so Maple needs to make the y
 range very large. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 
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{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 111 "At such a large range, w
e lose the finer detail. We can fix this problem by defining the y-ran
ge for ourselves." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 121 "The y range is given, after the x range,  as two numbers
 separated by 2 dots - just as the plot domains is defined for x." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
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DISCONTINUOUS GRAPHS" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 375 "The graph above has a flaw. There appears to be a vert
ical line at x = 1 when really the function is not defined at x = 1. T
his happens because Maple assumes graphs are continuous, which means t
here are no breaks or gaps in a smooth curve. So it tries to keep the \+
graph connected by drawing that extra line. We can fix this problem by
 telling Maple to expect discontinuities." }}{PARA 0 "" 0 "" {TEXT -1 
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{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 61 "Here is a
 way of graphing a family of functioins all at once." }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 89 "B1. Graph the functions x
^3, x^3 - 2*x, x^3 + 2*x on the same axes using domain x =-2..2 " }}
{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 0 "" }}{PARA 0 "" 0 "" {TEXT -1 88 "This single command \+
prints the functions x, x^2, x^3, ..., x^20 on the same set of axes." 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 117 "Protot
ype using parameter k.......$ : separates prototype from range....... \+
1..20 : range of values for the parameter" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 37 "plot( \{ x^k $ k = 1..20 \}, x = 0..1);" }}{PARA 13 "
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\"#:F*" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve
 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve
 8" "Curve 9" "Curve 10" "Curve 11" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 189 "B2. Copy and paste the three commands ab
ove, change f(x) as follows, and re-execute. What can you conclude by \+
these examples?\n     A. f(x) = | x | (hint : abs)                    \+
 B. f(x) =" }{XPPEDIT 19 1 "x^3;" "6#*$%\"xG\"\"$" }{TEXT -1 68 "     \+
         C. f(x) = sqrt(x)                           D. f(x) = " }
{XPPEDIT 19 1 "x^2(x^2+1);" "6#)%\"xG-\"\"#6#,&*$F$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 257 "
" 0 "" {TEXT -1 19 "OTHER GRAPH OPTIONS" }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}{PARA 0 "" 0 "" {TEXT -1 76 "There are quite a few options availa
ble. You can see them all by typing this" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "?plot[options]" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 179 "Also you
 can click on any graph and buttons will appear on the toolbar which a
lter the graph. By clicking on these buttons you can affect the appear
ance of the graph in some ways." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 83 "_______________________________________________
____________________________________" }}{PARA 4 "" 0 "" {TEXT -1 8 "C.
 Slope" }}{PARA 0 "" 0 "" {TEXT -1 83 "_______________________________
____________________________________________________" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 292 "Every non-vertical line has a slope. What exactly do lin
es with large and small positive and negative slopes look like? Using \+
the powerful graphing capabilities of Maple, we can see at a glance wh
at lines with different slopes look like. Here are the lines y = x, y \+
= 2x, y = 3x, ..., y = 20x" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "plot(\{ k*x $ k = 1..20 \}, x = -5.
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