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{SECT 0 {SECT 0 {PARA 257 "" 0 "" {TEXT 256 27 "Section 6: More on Gra
phing" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "with(plots):   with(student):" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 71 "The with(plots):  will load comman
ds for doing extra things with graphs" }}}{SECT 1 {PARA 4 "" 0 "" 
{TEXT -1 15 "Plotting points" }}{PARA 256 "" 0 "" {TEXT -1 0 "" }}
{PARA 297 "" 0 "" {TEXT 260 64 "    A point in Maple is defined using \+
square brackets:   [2, 3]." }}{PARA 258 "" 0 "" {TEXT -1 68 "To plot a
 point, tell Maple the list of points you want to plot.  A " }{TEXT 
361 4 "list" }{TEXT -1 104 " is defined using square brackets too!\nYo
u must use a list, even if there is only one point in the list." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
60 "plot( [ [1,3], [-4,5], [3.5,-1] ], x= -10..10, style=point);" }}}
{PARA 260 "" 0 "" {TEXT -1 0 "" }}{PARA 259 "" 0 "" {TEXT -1 152 "You \+
can make Maple color in a point on graph, by making a plot of the func
tion and a plot of the point and displaying them on the same graph, us
ing the " }{TEXT 256 7 "display" }{TEXT -1 95 " command.  \n\nWe'll gi
ve the plot of the function and the plot of the point a name, and use \+
the " }{TEXT 257 1 ":" }{TEXT -1 16 " rather than the" }{TEXT 258 2 " \+
;" }{TEXT -1 126 " since we don't want to see the plot yet. \n\nI've a
lso made use of some options to make the graph look a little better. (
Go to " }{TEXT 259 33 "Help...Topic Search: plot,options" }{TEXT -1 
14 " to see more.)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 10 "f:=x->x^2;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 33 "A:=plot(f(x), x=-5..5,color=red):" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 70 "B:=plot([ [3,f(3)] ], x=-5..5, style=point,
color=black,symbol=circle):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
13 "display(A,B);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 4 
"" 0 "" {TEXT 257 12 "Exercise 6.1" }}{PARA 0 "" 0 "" {TEXT -1 22 "Plo
t the function :   " }{TEXT 257 1 "g" }{TEXT -1 1 "(" }{TEXT 256 1 "x
" }{TEXT -1 4 ") = " }{XPPEDIT 18 0 "(x+50)^3-45*x^2+1;" "6#,(*$,&%\"x
G\"\"\"\"#]F'\"\"$F'*&\"#XF'*$F&\"\"#F'!\"\"\"\"\"F'" }{TEXT -1 34 "  \+
    and and plot a point at its " }{TEXT 345 1 "x" }{TEXT -1 12 "-inte
rcept. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 20 "" 0 "" 
{TEXT 259 21 "Student Workspace 6.1" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}}{SECT 1 {PARA 4 "" 0 
"" {TEXT -1 25 "Adding text to your plots" }}{PARA 298 "" 0 "" {TEXT 
-1 46 "You can also add text to your plots using the " }{TEXT 256 8 "t
extplot" }{TEXT -1 17 " command and the " }{TEXT 257 7 "display" }
{TEXT -1 195 " command.\nFor the textplot command, give the x and y co
ordinate for the location of the text and the text itself in quotes.\n
Text will be centered at the location given, unless you use the option
 " }{TEXT 258 5 "align" }{TEXT -1 49 " to justify the text. \nNotice a
ll commands end in" }{TEXT 362 1 " " }{TEXT 259 2 ": " }{TEXT -1 20 " \+
except for display." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 28 "P1:=plot(sin(x), x=0..2*Pi):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "P2:=plot([ [Pi/2, sin(Pi/2)] ], sty
le=point, symbol=circle, color=blue): " }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 53 "P3:=textplot( [2, 1, \"maximum\"],align=\{ABOVE,RIGHT
\}):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "display(P1,P2,P3);
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
62 "To see more options for the textplot command, type:  ?textplot" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{SECT 1 {PARA 4 "" 0 "" {TEXT 257 12 "Exercise 6.2" }}{PARA 
0 "" 0 "" {TEXT -1 22 "Plot the function :   " }{TEXT 257 1 "g" }
{TEXT -1 1 "(" }{TEXT 256 1 "x" }{TEXT -1 4 ") = " }{XPPEDIT 18 0 "(x+
50)^3-45*x^2+1;" "6#,(*$,&%\"xG\"\"\"\"#]F'\"\"$F'*&\"#XF'*$F&\"\"#F'!
\"\"\"\"\"F'" }{TEXT -1 18 " , a point at its " }{TEXT 259 1 "x" }
{TEXT -1 60 "-intercept and insert the text \"x-intecept\" near the po
int. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 20 "" 0 "" 
{TEXT 258 21 "Student Workspace 6.2" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 24 "Graphing discontinuiti
es" }}{PARA 258 "" 0 "" {TEXT -1 257 "Maple creates graphs a lot like \+
you might, it calculates a bunch of points, plots them and then connec
ts them. The problem with that is that dicontinuities sometimes don't \+
show up correctly.  Maple draws a line at x=-2, that is not really par
t of the graph." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "g:=x->1/(
x+2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "plot(g(x),x=-5..5,
y=-20..20);" }}}{PARA 259 "" 0 "" {TEXT -1 0 "" }}{PARA 296 "" 0 "" 
{TEXT -1 137 "You can let Maple know the graph should have a discontin
uity, and then it will graph it a little differently to handle the dis
continuity." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "plot(g(x),x=-
5..5, y=-20..20,discont=true);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 87 "   This problem is especially evident wit
h piecewise functions that are not continuous." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "h:=x->piecew
ise(x<3, x^2, x>=3, 5*x+1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
5 "h(x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "plot(h(x),x=-10
..10);" }}}{PARA 299 "" 0 "" {TEXT -1 180 "This graph looks a little f
ishy.  I see the parabola part of the graph to the left of 3 and the l
inear part to the right of 3, but are these parts really supposed to b
e connected? " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 46 "plot(h(x),x=-10..10, discont=true,color=blue);" 
}}}{PARA 0 "" 0 "" {TEXT -1 56 "     As you can see, the graph is real
ly NOT continuous." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 4 
"" 0 "" {TEXT 257 12 "Exercise 6.3" }}{PARA 0 "" 0 "" {TEXT -1 13 "The
 function " }{TEXT 354 1 "f" }{TEXT -1 2 " (" }{TEXT 355 1 "x" }{TEXT 
-1 7 ")  =   " }{XPPEDIT 18 0 "(x+1)/(x^2-1);" "6#*&,&%\"xG\"\"\"F&F&
\"\"\",&*$)F%\"\"#F'F&!\"\"F&!\"\"" }{TEXT -1 153 "   should have disc
ontinuities.  Explain where the discontinuities are and what they will
 look like (Do this WITHOUT Maple).   Type in your answer below." }}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 5 "Plot " }
{TEXT 356 1 "f" }{TEXT -1 2 " (" }{TEXT 357 1 "x" }{TEXT -1 12 ") usin
g the " }{TEXT 358 7 "discont" }{TEXT -1 61 " option.  \nNote: Maple d
oesn't usually pick a good range for " }{TEXT 359 1 "y" }{TEXT -1 53 "
 when there is an asymptote, so you should adjust the" }{TEXT 360 2 " \+
y" }{TEXT -1 42 " range to get a good viewing of the graph." }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 52 "Does the graph display the discontinuities? Explain." }}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 70 "Re-plot
 the graph and include a point to show the other discontinuity." }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 4 "" 0 "
implicitplot( )" {TEXT -1 14 "Implicit Plots" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 90 "Maple can plot curves that are \+
implicitly defined by an equation in the variables x and y." }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 266 10 "Example 1:" }}
{PARA 0 "" 0 "" {TEXT -1 58 "To plot the graph of the hyperbola given \+
by the equation: " }{XPPEDIT 18 0 "x^2/4 - y^2/9 = 1" "6#/,&*&%\"xG\"
\"#\"\"%!\"\"\"\"\"*&%\"yG\"\"#\"\"*F)F)\"\"\"" }{TEXT -1 9 " use the \+
" }{TEXT 271 15 "implicitplot( )" }{TEXT -1 94 " command. To use this \+
command we must first load the \"plots\" library using the \"with\" co
mmand." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 50 "Note the \+
syntax for this command on the next line." }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 44 "implicitplot(x^2/4-y^2/4=1,x=-5..5,y=-5..5);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT 
267 10 "Example 2:" }}{PARA 0 "" 0 "" {TEXT 268 20 "Graph the equation
  " }{XPPEDIT 18 0 "x^2/25+y^2/9=1" "6#/,&*&%\"xG\"\"#\"#D!\"\"\"\"\"*
&%\"yG\"\"#\"\"*F)F*\"\"\"" }{TEXT 269 36 " using the implicitplot( ) \+
command. " }}{PARA 0 "" 0 "" {TEXT -1 121 "Recall that this is the equ
ation of an ellipse with the lengths of major and minor axes equal to \+
10 and 6 respectively.  " }}{PARA 0 "" 0 "" {TEXT -1 66 "Our first att
empt at getting the expected graph comes up short !  " }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 45 "implicitplot(x^2/25+y^2/9=1,x=-5..5,y=-5.
.5);" }}}{PARA 0 "" 0 "" {TEXT -1 47 "Why did we get a circle instead \+
of an ellipse ?" }}{PARA 0 "" 0 "" {TEXT -1 110 "The problem here is t
hat the x and y scales are not equal. To force equal scaling add \"sca
ling=constrained\" . " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "imp
licitplot(x^2/25+y^2/9=1,x=-5..5,y=-5..5,scaling=constrained);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 4 "" 0 "" 
{TEXT 273 12 "Exercise 6.2" }}{PARA 0 "" 0 "" {TEXT 272 19 "Graph the \+
equation " }{XPPEDIT 18 0 "x^2+4*y^2=4" "6#/,&*$%\"xG\"\"#\"\"\"*&\"\"
%F(*$%\"yG\"\"#F(F(\"\"%" }{TEXT 276 1 " " }}{SECT 1 {PARA 20 "" 0 "" 
{TEXT 274 21 "Student Workspace 6.2" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{PARA 4 "" 0 "" {TEXT 
-1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" 
{TEXT -1 12 "Plot Options" }}{PARA 0 "" 0 "" {TEXT -1 177 "There are m
any options available when you use the plot command.  To see a list ex
ecute the next line to go directly to Maple's Help Page on this comman
d.  Skip this if you wish." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
15 "?plot[options];" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 2 0 0" 15 }{VIEWOPTS 
1 1 0 1 1 1803 }