{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 Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 23 "Courier" 1 10 0 0 0 0 0 0 0 0 0 0 3 0 0 1 }{CSTYLE " " -1 256 "" 0 1 0 0 0 1 1 2 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 260 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 261 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 265 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 266 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 267 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 268 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 269 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 270 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 271 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 272 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 273 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 274 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 275 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 276 "" 1 12 0 0 0 0 1 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 277 "" 1 12 0 0 0 0 1 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 278 "" 1 12 0 0 0 0 1 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 279 "" 1 12 0 0 0 0 1 0 1 0 0 0 0 0 0 1 } {CSTYLE "" -1 280 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 281 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 282 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 283 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 284 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 } {CSTYLE "" -1 285 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 286 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 287 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 288 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 289 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 290 "" 0 1 0 128 0 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 291 "" 0 1 0 128 0 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 292 "" 0 1 0 128 0 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 293 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 294 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 } {CSTYLE "" -1 295 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 296 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 297 "" 1 12 0 0 0 0 1 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 298 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 299 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 } {CSTYLE "" -1 300 "" 0 1 0 0 0 1 0 2 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 301 "" 0 1 0 0 0 1 1 2 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 302 "" 0 1 0 0 0 1 1 2 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 303 "" 0 1 0 0 0 1 1 2 1 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 0 }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 0 }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 0 }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 0 }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 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 257 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 1 1 1 1 }1 1 0 0 6 6 1 0 1 0 1 2 0 1 }} {SECT 0 {SECT 0 {PARA 257 "" 0 "" {TEXT 256 12 "Section 3: G" }{TEXT 303 0 "" }{TEXT 302 7 "raphing" }}{PARA 0 "" 0 "" {TEXT -1 266 "In thi s section you will learn how to plot the graph of a function defined b y an expression. Other topics covered include: combining the graphs of several expressions into a single plot, plotting points, and combinin g different plot structures into a single picture." }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{SECT 1 {PARA 4 "" 0 "plot( )" {TEXT -1 28 "Plotting an Expression: the " }{TEXT 295 7 "plot( )" } {TEXT -1 8 " command" }}{PARA 0 "" 0 "" {TEXT 280 10 "Example 1:" }} {PARA 0 "" 0 "" {TEXT -1 11 "We use the " }{TEXT 298 7 "plot( )" } {TEXT -1 31 " command to plot the graph of " }{XPPEDIT 18 0 "3*x^2-8 " "6#,&*&\"\"$\"\"\"*$%\"xG\"\"#F&F&\"\")!\"\"" }{TEXT -1 5 " for" } {TEXT 257 2 " x" }{TEXT -1 20 " between - 5 and 5 ." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plot(3*x^2-8,x=-5..5);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 29 "Notice that Maple scales the " }{TEXT 258 1 "y " }{TEXT -1 32 "-axis automatically, choosing a " }{TEXT 259 1 "y" } {TEXT -1 74 "-scale that shows the entire graph corresponding to the s pecified domain. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 149 "You can override automatic y-scaling by specifying a ran ge for y as well as x. On the next line we have limited the y-range to the interval [-20,40]." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "p lot(3*x^2-8,x=-5..5,y=-20..40);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 261 "If you click on a graph with the left mouse button, the graph \+ is selected and the bottom toolbar options are changed. See the refer ence diagram below. Now when you click on the graph, the point coordi nates of its location are shown. The 1:1 button makes the " }{TEXT 260 1 "x" }{TEXT -1 11 "-scale and " }{TEXT 261 1 "y" }{TEXT -1 15 "-s cale equal. " }}{PARA 0 "" 0 "" {TEXT -1 12 "Scroll back " }{TEXT 262 2 "up" }{TEXT -1 96 " to the previous graph and experiment with th ese features. Try the other graph options as well." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 282 10 "Example 2:" }}{PARA 0 " " 0 "" {TEXT -1 87 "Automatic scaling is a useful feature but there ar e times when you may want to set the " }{TEXT 281 1 "y" }{TEXT -1 102 " range manually. For example automatic scaling isn't appropriate for \+ graphs with vertical asymptotes. " }}{PARA 0 "" 0 "" {TEXT -1 122 "Com pare the next two graphs. Notice how we have set the limits for y to t he interval [-20,20] in the second plot command. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plot(x/(x-2),x=-5..5);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "plot(x/(x-2 ),x=-5..5,y=-20..20);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT 283 10 "Example 3:" }}{PARA 0 "" 0 "" {TEXT -1 20 "Plot the graph of " }{XPPEDIT 18 0 "y=x^3+1-exp(x)" "6#/%\"yG,(*$%\"xG\"\"$ \"\"\"F)F)-%$expG6#F'!\"\"" }{TEXT -1 88 " over the domain [-8,8]. Cho ose a y-range that allows you to see the four x-intercepts." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 65 "First let's tak e a look at the plot with automatic scaling of y. " }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 27 "plot(x^3+1-exp(x),x=-8..8);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 119 "The large negative values for y near 8 have forced the vertical scale to be too large to see the x-intercepts clearly. " }}{PARA 0 "" 0 "" {TEXT -1 60 "A bett er view is achieved by setting limits on the y-range. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "plot(x^3+1-exp(x),x=-8..8,y=-5..15) ;" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 276 12 "Exercise 3.1" }}{PARA 0 "" 0 "" {TEXT -1 23 "Plot y = sin(x) over " }{TEXT 263 3 "two" }{TEXT -1 18 " complete periods." }}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 21 "Student Workspace 3.1" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 10 "Answer 3.1" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "plot (sin(x), x=-2*Pi..2*Pi);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}}}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{SECT 1 {PARA 4 "" 0 "" {TEXT 277 12 "Exercise 3.2" }}{PARA 0 "" 0 "" {TEXT -1 6 "Plot " }{XPPEDIT 18 0 "y = 3*x^4-6*x^2 " "6#/%\"yG,&*&\"\"$\"\"\"*$%\"xG\"\"%F(F(*&\"\"'F(*$F*\"\"#F(!\"\"" } {TEXT -1 41 " over the domain [-10,10] with automatic " }{TEXT 264 1 " y" }{TEXT -1 124 " scaling. After observing the graph, edit the domai n and range so that you can see the x-intercepts clearly. Estimate th e " }{TEXT 272 1 "x" }{TEXT -1 34 "-intercepts with the mouse cursor. " }}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 21 "Student Workspace 3.2" }} {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 "" }}}}{SECT 1 {PARA 5 "" 0 " " {TEXT -1 10 "Answer 3.2" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "plot(3*x^4-6*x^2,x);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 17 "Notice how large " }{TEXT 265 1 "y" }{TEXT -1 15 " b ecomes when " }{TEXT 270 1 "x" }{TEXT -1 11 " = -10 or " }{TEXT 271 1 "x" }{TEXT -1 23 " = 10; with automatic " }{TEXT 266 1 "y" }{TEXT -1 61 " scaling it is difficult to see how the function behaves for " }{TEXT 269 1 "x" }{TEXT -1 53 " between -2 and 2. In the next plot we restrict the " }{TEXT 267 1 "y" }{TEXT -1 57 " scale in order to bett er observe the behavior for small " }{TEXT 268 1 "y" }{TEXT -1 9 " out puts." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "plot (3*x^4-6*x^2,x =-3..3,y=-5..15);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 " " {TEXT -1 4 "The " }{TEXT 273 1 "x" }{TEXT -1 38 "-intercepts are abo ut -1.4, 1.4 and 0." }}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 29 "Plottin g Several Expressions " }}{PARA 0 "" 0 "" {TEXT -1 102 "To show more t han one graph in the same picture list them in square brackets [ ] se parated by commas." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "plot([ cos(x),x^2],x=-1..4,y=-4..4);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 313 "Notice that each of the graphs is displayed using a different color. You can specify the colors for eac h function by adding a color option at the end of the command. The col ors are assigned in the same order as the functions. Note that the col ors must also be listed in a square bracket [ ] . Here is an example. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "plot([cos(x),x^2],x=-1. .5,y=-4..4,color=[blue,black]);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "Here are the colors available in M aple. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 23 214 "aquamarine black blue navy coral cyan \nbrown gold \+ green gray grey khaki \nmagenta maroon orange pink pl um red \nsienna tan turquoise violet wheat white \nyellow \+ " }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 278 12 "Exercise 3.3" }}{PARA 0 "" 0 "" {TEXT -1 20 "Graph the functions " }{XPPEDIT 18 0 "y = x^2-5*x+6" "6#/%\"yG,(*$%\"xG\"\"#\"\"\"*&\"\"&F)F'F)!\"\"\"\"'F)" }{TEXT -1 7 " and " }{XPPEDIT 18 0 "y= 1/(x-2)^2" "6#/%\"yG*&\"\"\"F &*$,&%\"xGF&\"\"#!\"\"F*F+" }{TEXT -1 97 " together. Experiment with d ifferent y ranges so that complete pictures of both graphs are shown. " }}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 21 "Student Workspace 3.3" }} {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 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 5 "" 0 " " {TEXT -1 10 "Answer 3.3" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "y1:=x^2-5*x+6;" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "y2:=1/(x-2)^2;" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "plot([y1,y2],x=-3..8 ,y=-1..6);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 15 "Plotting points" }}{PARA 0 "" 0 "" {TEXT -1 50 "The \+ plot command can also plot one or more points." }}{PARA 0 "" 0 "" {TEXT 284 10 "Example 1:" }}{PARA 0 "" 0 "" {TEXT -1 22 "Plot the poin t (2,3) ." }}{PARA 0 "" 0 "" {TEXT -1 67 "Note in the following line t hat we use two sets of square brackets." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "plot([ [2,3] ],style=point);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT 285 10 "Example 2:" }}{PARA 0 " " 0 "" {TEXT -1 103 "We can control the size of the x and y ranges sho wn by adding these to the command as in the next line." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "plot([ [2,3] ],x=-7..7,y=-7..7,styl e=point);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT 286 10 "Example 3:" }}{PARA 0 "" 0 "" {TEXT -1 172 "To graph more than one point list them in the plot command. Note the commas. Remember sq uare brackets for each point and an extra pair of square brackets surr ound the list." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "plot([ [2, 3],[-2,5],[1,-4] ],x=-7..7,y=-7..7,style=point);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT 287 10 "Example 4:" }}{PARA 0 " " 0 "" {TEXT -1 66 "Changing style to \"line\" connects the points in \+ the order listed. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "plot([ [2,3],[-2,5],[1,-4] ],x=-7..7,y=-7..7,style=line);" }}{PARA 13 "" 1 " " {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT 288 10 "Example 5:" }}{PARA 0 "" 0 "" {TEXT -1 131 "Optional extensions can be used to specify poi nt color and symbol (e.g. diamond, circle, cross is default) to indica te the points. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "plot([[3, 2],[-2,3],[2,-1]],style=point,color=blue,symbol=circle);" }}{PARA 13 " " 1 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT 297 12 "Exercise 3.4" }}{PARA 0 "" 0 "" {TEXT -1 108 "Plot the following points using \+ the color red and the diamond symbol: [1,4] , [-2,-3], [4,-5] and [-6 ,5] . " }}{PARA 0 "" 0 "" {TEXT -1 62 "Then connect the points with li nes in a separate plot command." }}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 21 "Student Workspace 3.4" }}{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 5 "" 0 "" {TEXT -1 10 "Answ er 3.4" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "plot([[1,4],[-2,-3 ],[4,-5],[-6,5]],style=point,color=red,symbol=diamond);" }}{PARA 13 " " 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "plot ([[1,4],[-2,-3],[4,-5],[-6,5]],style=line,color=red,symbol=diamond);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}}}}{SECT 1 {PARA 4 "" 0 "with(plot s)" {TEXT -1 48 "Combining Graphs of Expressions and Points: the " } {TEXT 296 10 "display( )" }{TEXT -1 8 " command" }}{PARA 0 "" 0 "" {TEXT -1 34 "A special plotting package called " }{TEXT 290 5 "plots" }{TEXT -1 122 " contains many additional graphing features. To use t hese commands, you need to execute the following line which loads " } {TEXT 291 5 "plots" }{TEXT -1 148 ". Recall, the colon at the end of \+ the statement allows this line to be executed without displaying any d istracting output. To see the contents of " }{TEXT 292 5 "plots" } {TEXT -1 41 " you can change the colon to a semicolon." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{PARA 0 "" 0 "" {TEXT -1 4 "The " }{TEXT 289 11 "display( ) " }{TEXT -1 173 "command a llows you to combine graphs of expressions and points in the same pict ure. The first step is to name the individual picture components. IMPO RTANT: Be sure to use a " }{TEXT 294 5 "colon" }{TEXT -1 79 " at the e nd of the line to suppress output (see first three lines below). The \+ " }{TEXT 293 11 "display( ) " }{TEXT -1 74 "command is then used to do the actual plot (this ends with a semicolon). " }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 " pict1:=plot([-3*x+5,9-x^2],x=-3..5,color=[green,red]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "pict2:=plot([[-1,8],[4,-7]],style=p oint,color=blue,symbol=circle):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "display([pict1,pict2]);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}} {PARA 0 "" 0 "" {TEXT -1 130 "Alternatively we can list these three re lated plot commands in a single execution group by typing SHIFT-ENTER \+ at end of each line." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "pict 1:=plot([-3*x+5,9-x^2],x=-3..5,color=[green,red]):" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 66 "pict2:=plot([[-1,8],[4,-7]],style=point,color=blue, symbol=circle):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "display([pict1,p ict2]);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 22 "For more on this see \"" }{TEXT 299 0 "" }{TEXT 256 45 "Execution \+ groups with more than one command\" " }{TEXT 300 14 "in the section" } {TEXT 301 40 " Notes on the Maple Worksheet Interface " }{TEXT 257 1 " " }{TEXT -1 28 "at the end of this tutorial." }}{SECT 1 {PARA 4 "" 0 "" {TEXT 279 12 "Exercise 3.5" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 47 "D isplay a graph that contains both the function" }{MPLTEXT 1 0 1 " " } {XPPEDIT 18 0 "y = x^2+x-6" "6#/%\"yG,(*$%\"xG\"\"#\"\"\"F'F)\"\"'!\" \"" }{TEXT -1 10 " and its " }{TEXT 274 1 "x" }{TEXT -1 5 " and " } {TEXT 275 1 "y" }{TEXT -1 33 " intercepts, marked with circles." }}} {SECT 1 {PARA 5 "" 0 "" {TEXT -1 21 "Student Workspace 3.5" }}{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 5 "" 0 "" {TEXT -1 10 "Answer 3.5" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 37 "pict4:=plot(x^2+x-6,x=-5..4,y=-8..8):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "pict5:=plot([[0,-6],[-3,0],[ 2,0]],style=point,symbol=circle, color=blue):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "display([pict4,pict5]);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}}}}}}{MARK "0 3" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }