{VERSION 5 0 "IBM INTEL NT" "5.0" } {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 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 266 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 267 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 269 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 271 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 272 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 273 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 274 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 275 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 276 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 277 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 278 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 279 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 280 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 281 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 282 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 283 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 284 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 285 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 286 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 287 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 288 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 289 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 290 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 291 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 292 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 293 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 294 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 295 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 296 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 297 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 298 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 299 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 300 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Ti mes" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Maple Plot" -1 13 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 }} {SECT 0 {EXCHG {PARA 3 "" 0 "" {TEXT -1 31 "Exam 3 - Keys for Practice Exam" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 29 "P. 543 - (Quadratic Equ ation)" }}{EXCHG {PARA 0 "" 0 "" {TEXT 256 19 "1. Solve 2*x^2-7=0" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "solve(2*x^2-7=0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,$*$-%%sqrtG6#\"#9\"\"\"#F)\"\"#,$F$#!\"\"F+" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 257 25 "2. Solve 14*x^2 + 5*x = 0" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "solve(14*x^2 + 5*x = 0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"!#!\"&\"#9" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 258 24 "3. Solve x^2-12*x+36 = 9" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "x^2 - 12*x + 36 = 9;\nx^2 - 12*x + 36 - 9 = 0;\nsolve(x^2 - 12 *x + 27 = 0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,(*$)%\"xG\"\"#\"\" \"F)*&\"#7F)F'F)!\"\"\"#OF)\"\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/, (*$)%\"xG\"\"#\"\"\"F)*&\"#7F)F'F)!\"\"\"#FF)\"\"!" }}{PARA 11 "" 1 " " {XPPMATH 20 "6$\"\"*\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 259 37 "9 . Complete the square for x^2 - 12*x" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "x^2 - 12*x:\nx^2 - 12*x + 36 - 36:\nfactor(x^2-12*x+36) - 36;" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$),&%\"xG\"\"\"\"\"'!\"\"\"\"#F(F( \"#OF*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 260 33 "23. Graph f(x) = -3 * \+ (x+2)^2 + 4" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "expand(-3*(x+2)^2+4) ;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)%\"xG\"\"#\"\"\"!\"$*&\"#7 F(F&F(!\"\"\"\")F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 107 "The x-coor d. of vertex is 12 / (-6) = -2. The y intercept is y=-8. To find x-in tercept, we solve for zero:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "solve(-3*x^2-12*x-8=0);\neva lf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,&!\"#\"\"\"*&#\"\"#\"\"$F%* $-%%sqrtG6#F)F%F%!\"\",&F$F%*&#F(F)F%F+F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$$!+R0qaJ!\"*$!*h%*HX)F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "plot(-3*x^2-12*x-8, x=-6..2);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$7S7$$!\"'\"\"!$!#WF*7 $$!37nmmmFiDe!#<$!3e)\\^e'oh!*R!#;7$$!35LLLo!)*Qn&F0$!3G>5&\\5e#\\OF37 $$!3AmmmwxE.bF0$!31-$4X`l=G$F37$$!3YmmmOk]J`F0$!3oGaET0oHHF37$$!3_LLL[ 9cg^F0$!3;psg+Yu'f#F37$$!3GmmmhN2-]F0$!3&\\R(*3qLPI#F37$$!3!******\\`o z$[F0$!3I9]p@'>i,#F37$$!3Cnmm\")3DoYF0$!3;%[a-$)oet\"F37$$!3u*****\\^x !*\\%F0$!3esNzFlht9F37$$!3BLLL8>1DVF0$!3*z(*\\-(Qx@7F37$$!3kmmmw))yrTF 0$!3B>RWx++:5F37$$!3;+++S(R#**RF0$!3c1e)Rhy3*zF07$$!30++++@)f#QF0$!3kK 7c))=j-gF07$$!3-+++gi,fOF0$!3aiJ$G&[+dUF07$$!3qmmm\"G&R2NF0$!3$[zsbg@n \"GF07$$!3XLLLtK5FLF0$!3yYhF%H4OG\"F07$$!3eLLL$HsV<$F0$!3U:)p/]3XP\"!# =7$$!3?+++b)4n*HF0$\"3VKw$[R3(>5F07$$!3rLLL$\\[%RGF0$\"3g(=@6oyf)=F07$ $!3#)*****\\&y!pm#F0$\"3%y*y\")QF0 7$$!3j+++v@825F0$\"3&3JRiWSE/\"F07$$!352+++d\"3F)F^q$!3C,*4IIH@F\"F^q7 $$!3'*QLLL4)Hl'F^q$!3'>!*y*QvGW8F07$$!3c,+++qfD\\F^q$!3\")oA>u(Gr\"GF0 7$$!3Kqmm;/LgLF^q$!3#>Dv_6ejI%F07$$!3M,+++13\\;F^q$!3x*))eZG(o-hF07$$! 3'R:n'F^q$!3Nonl%*)4Tt\"F37$$\"31JLLLSDo$)F^q$!3^)>*p5NF9?F37 $$\"3ammm^Q405F0$!3NSu> " 0 "" {MPLTEXT 1 0 0 "" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$$!+R0qaJ!\"*$!*h%*HX)F%" }}{EXCHG {PARA 0 "" 0 "" {TEXT 261 31 "24. Graph f(x) = 2*x^2 -12*x+23" }} {PARA 0 "" 0 "" {TEXT -1 107 "The x-coord. of vertex is 12/4 = 3. The \+ y-intercept is y = 23. To find the x-intercepts, we solve for zero:" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "solve(2*x^2 -12*x+23 = 0); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,&\"\"$\"\"\"*&^##F%\"\"#F%-%%sqrt G6#\"#5F%F%,&F$F%*&^##!\"\"F)F%F*F%F%" }}}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 97 "The solutions are imaginary nu mbers, so no intersections with x-axis. The final graph looks like:" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "plot(2*x^2 -12*x+23,x=0..6 );" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG 6$7S7$$\"\"!F)$\"#BF)7$$\"3%*******\\#HyI\"!#=$\"3E6VpC8[Y@!#;7$$\"33+ +]([kdW#F/$\"3BKmN*yr%=?F27$$\"3++++v;\\DPF/$\"3k))4Wv&*p!)=F27$$\"3W+ ++D1E?\"F27$$\"33+++lN?c7FY$\"3mTPM,_;36F27$$\"3-++]U$e6P\"FY$\"3`p9/H]i I5F27$$\"36+++&>q0]\"FY$\"3![nW-[zl\\*FY7$$\"3'******\\U80j\"FY$\"3Oh/ @ep)4v)FY7$$\"35+++0ytboP'4)FY7$$\"3)****\\(QNXp=FY$\"3G 'z*3-1FcvFY7$$\"3.+++XDn/?FY$\"3]^NN&[`8)pFY7$$\"3.+++!y?#>@FY$\"3'*=w woSa^lFY7$$\"3'****\\(3wY_AFY$\"3^')e$>N4w6'FY7$$\"3#)******HOTqBFY$\" 3'GbzX*zv#z&FY7$$\"37++v3\">)*\\#FY$\"3v)GVz%=O+bFY7$$\"3:++DEP/BEFY$ \"3Il*QY1#>%G&FY7$$\"3=++](o:;v#FY$\"3<#>#RL&*QB^FY7$$\"3=++v$)[opGFY$ \"3z.l/fS'R.&FY7$$\"3%*****\\i%Qq*HFY$\"3*3t39a<++&FY7$$\"3&****\\(QIK HJFY$\"3GnIq'*)[M.&FY7$$\"3#****\\7:xWC$FY$\"3dEm'\\:Q&>^FY7$$\"37++]Z n%)oLFY$\"3;gEGYe4s_FY7$$\"3y******4FL(\\$FY$\"3)4*=()['zY\\&FY7$$\"3# )****\\d6.BOFY$\"3#)z:VYcLwdFY7$$\"3(****\\(o3lWPFY$\"3Kf-mK)4!4hFY7$$ \"3!*****\\A))ozQFY$\"3iuG')[[qZlFY7$$\"3e******Hk-,SFY$\"3!*)3w7&FY$\"3`*>7lc_`S\"F27$$\"3O++v)Q?QD&FY$\"3AS !\\*o7%f^\"F27$$\"3G+++5jyp`FY$\"3[%o75VxJi\"F27$$\"3<++]Ujp-bFY$\"3mw Db'z(p_$[dFY$\"3w^zO M@l5?F27$$\"37++D6EjpeFY$\"3'))*)4ZEep9#F27$$\"\"'F)F*-%'COLOURG6&%$RG BG$\"#5!\"\"F(F(-%+AXESLABELSG6$Q\"x6\"Q!Fb[l-%%VIEWG6$;F(Fez%(DEFAULT G" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 1 "Curve 1" } }}}{EXCHG {PARA 0 "" 0 "" {TEXT 262 53 "25. Find x and y intercepts fo r f(x) = x^2 - 9*x + 14" }}{PARA 0 "" 0 "" {TEXT -1 81 "The y-intercep t is 14 (always easy). To find the x-intercepts, we solve for zero:" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "solve(x^2 - 9*x + 14 = 0);" }} {PARA 0 "" 0 "" {TEXT -1 1 "\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\" (\"\"#" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 47 "P. 544 - (Quadratic E quations and Inequalities)" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 263 23 "1. Solve 3*x^2 - 16 = 0" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "solve(3*x^2 - 16 = 0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,$*$-%%sqrtG6#\"\"$\"\"\"#\"\"%F(,$F$#!\"%F(" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 264 36 "2. Solve 4*x*(x-2) - 3*x*(x+1) = \+ -18" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "expand(4*x*(x-2) - 3*x*(x+1) = -18);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&*$)%\"xG\"\"#\"\"\"F)*& \"#6F)F'F)!\"\"!#=" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "solve (x^2 - 11*x + 18 = 0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"*\"\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 265 24 "3. Solve x^2 + x + 1 = 0" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "solve(x^2+x+1=0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,&#!\"\"\"\"#\"\"\"*&^##F'F&F'-%%sqrtG6#\"\"$F'F',&F $F'*&^#F$F'F+F'F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 266 37 "8. Complete the square for x^2 + 14*x" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "x^2 + 14*x:\nx^2 + 14*x + 49 - 49:\nfactor(x^2 + 14*x + 49) - 49;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$),&%\"xG\"\"\"\"\"(F(\"\"#F(F(\"#\\!\"\" " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 267 30 "16. Graph f(x) = 4*(x-2)^2 + 5" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "expand(4*(x-2)^2 + 5);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)%\"xG\"\"#\"\"\"\"\"%*&\"#;F(F&F( !\"\"\"#@F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "plot(4*x^2-1 6*x+21,x=0..4);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$7S7$$\"\"!F)$\"#@F)7$$\"3Hmmmm;')=()!#>$\"3GKQGb*QN'>!# ;7$$\"3RLLLe'40j\"!#=$\"3wR.l,Fv\\=F27$$\"3mmmm;6m$[#F6$\"3#45.:^)GF(>%F6$\"3%)*3po'[\"*) \\\"F27$$\"3Qmmm\">K'*)\\F6$\"3b)zlpcW7S\"F27$$\"3P*****\\Kd,\"eF6$\"3 l/]cSlS08F27$$\"3-mmm\"fX(emF6$\"3U%\\^nFc>@\"F27$$\"3.*****\\U7Y](F6$ \"3`dyfU)QX7\"F27$$\"3'QLLLV!pu$)F6$\"37EL3!H\"fS5F27$$\"3xmmm;c0T\"*F 6$\"3rhI\"[#pm;(*!#<7$$\"3#*******H,Q+5F`o$\"3Eo_*z`fp**)F`o7$$\"3)*** ****\\*3q3\"F`o$\"3p4/_H1@M$)F`o7$$\"3)*******p=\\q6F`o$\"3_(QW4&\\L_x F`o7$$\"3mmm;fBIY7F`o$\"3%)H4>N0CssF`o7$$\"3GLLLj$[kL\"F`o$\"3M[?4)4.7 w'F`o7$$\"3?LLL`Q\"GT\"F`o$\"3E$**[LG]\"zjF`o7$$\"3!*****\\s]k,:F`o$\" 3%>7a]`IM*fF`o7$$\"39LLL`dF!e\"F`o$\"3a.'fHxtYq&F`o7$$\"33++]sgam;F`o$ \"3J,21(3mZW&F`o7$$\"3/++]F`o$\"3S,!3ZF!>I]F`o7$$\"3immmTc-)*>F `o$\"3R8LO#f:++&F`o7$$\"3Mmm;f`@'3#F`o$\"3m]\\i_BtH]F`o7$$\"3y****\\nZ )H;#F`o$\"3E:\"[x8ci5&F`o7$$\"3YmmmJy*eC#F`o$\"3stMZuH'=C&F`o7$$\"3')* *****R^bJBF`o$\"3*)y;WV_rRaF`o7$$\"3f*****\\5a`T#F`o$\"37,9;Ih2!p&F`o7 $$\"3o****\\7RV'\\#F`o$\"3aG-#z^'y&)fF`o7$$\"3k*****\\@fke#F`o$\"3yiOV VwtvjF`o7$$\"3/LLL`4NnEF`o$\"3AK'f'z\"H9y'F`o7$$\"3#*******\\,s`FF`o$ \"3s)3k!eiPssF`o7$$\"3[mm;zM)>$GF`o$\"3)R3D%QgyoxF`o7$$\"3$*******pfa< HF`o$\"3qfHDGCcn$)F`o7$$\"3#HLLeg`!)*HF`o$\"3WowY+SW%)*)F`o7$$\"3w**** \\#G2A3$F`o$\"3ENT=4/p%o*F`o7$$\"3;LLL$)G[kJF`o$\"3CD0Ba\"3C/\"F27$$\" 3#)****\\7yh]KF`o$\"3x8p!H'R'>F27$$\"\"%F)F*-%'COLOU RG6&%$RGBG$\"#5!\"\"F(F(-%+AXESLABELSG6$Q\"x6\"Q!Fc[l-%%VIEWG6$;F(Ffz% (DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 1 "Cu rve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT 268 52 "18. Find x-and y-inter cept(s) of f(x) = x^2 - x - 6." }{TEXT -1 52 " The y-intercept is -6, \+ for the x-intercept we solve" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "sol ve(x^2 - x - 6 = 0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"$!\"#" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 269 24 "23. Solve x^2 + 5*x <= 6" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "solve(x^2 + 5*x <= 6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%*RealRangeG6$!\"'\"\"\"" }}}{EXCHG {PARA 0 " " 0 "" {TEXT 270 21 "24. Solve x - 1/x > 0" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 22 "x - 1/x = (x^2 - 1)/x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&%\"xG\"\"\"*&F&F&F%!\"\"F(*&,&*$)F%\"\"#F&F&F&F(F&F% F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "solve((x^2 - 1)/x > 0 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$-%*RealRangeG6$-%%OpenG6#!\"\"-F '6#\"\"!-F$6$-F'6#\"\"\"%)infinityG" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 31 "P. 539 - (Solving Inequalities)" }}{EXCHG {PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 271 18 "6. x^2 + x - 2 < 9" } {TEXT -1 30 " - first solve x^2 + x -11 = 0" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "solve(x^2 + x - 2 < 9);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%*RealRangeG6$-%%OpenG6#,&#!\"\"\"\"#\"\"\"*&#\"\"$F,F-*$-%%sqr tG6#\"\"&F-F-F+-F'6#,&F*F-*&#F0F,F-F2F-F-" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 272 14 "8. 4-x^2 >= 0 " }{TEXT -1 30 "- special points are -2 an d +2" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "solve(4-x^2 >= 0);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%*RealRangeG6$!\"#\"\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 273 22 "10. x^2 + 6*x + 9 < 0 " }{TEXT -1 17 "- \+ has no solution" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "solve(x^2 + 6*x \+ + 9 < 0);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 274 20 "14. 5x(x+1)(x-1) > \+ 0" }{TEXT -1 35 " - special points are 0, -1, and 1." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "solve(5*x*(x+1)*(x-1) > 0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$-%*RealRangeG6$-%%OpenG6#!\"\"-F'6#\"\"!-F$6$-F'6#\"\" \"%)infinityG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 275 23 "15. (x+3)(x-2)( x+1) > 0" }{TEXT -1 35 " - special points are -3, 2, and -1" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "solve((x+3)*(x-2)*(x+1) > 0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$-%*RealRangeG6$-%%OpenG6#!\"$-F'6#!\"\"-F$6$ -F'6#\"\"#%)infinityG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 276 20 "21. (x+ 1)/(x-5) >= 0" }{TEXT -1 30 " - special points are -1 and 5" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "solve((x+1)/(x-5) >= 0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$-%*RealRangeG6$,$%)infinityG!\"\"F(-F$6$-%%OpenG6# \"\"&F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 277 27 "27. (x-2) (x+1) / (x- 5) <=0" }{TEXT -1 34 " - special points are 2, -1, and 5" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "solve((x-2)*(x+1)/(x-5) <= 0);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6$-%*RealRangeG6$,$%)infinityG!\"\"F(-F$6$\"\"#-%% OpenG6#\"\"&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 278 27 "28. (x+4)(x-1) / (x+3) >= 0" }{TEXT -1 35 " - special points are -4, 1, and -3" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "solve((x+4)*(x-1)/(x+3) >= 0);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$-%*RealRangeG6$!\"%-%%OpenG6#!\"$-F$6$ \"\"\"%)infinityG" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 27 "P. 528 - ( Max/Min Programs)" }}{EXCHG {PARA 0 "" 0 "" {TEXT 279 167 "1. If x is \+ the number of months after January 2001, the a certain share price is \+ V(x) = x^2 - 6*x + 13. What's the lowest value V will reach, and when \+ will that occur?" }{TEXT -1 62 " It's a parabola, opening up, so the m inimum is at the vertex:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "x := 6/ 2;\nV(x) := x^2 - 6*x + 13;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG \"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"VG6#\"\"$\"\"%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 280 188 "4. Profit is the difference between revenue R(x) and co st C(x). Given that R(x) = 1000*x - x^2 and C(x) = 3000 + 20*x, find t he total profit, the maximum profit, and for which x it occurs." }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "restart;\nR(x) := 1000*x-x^2;\nC(x) := 3000 + 20*x;\nP(x) := R(x) - C(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"RG6#%\"xG,&F'\"%+5*$)F'\"\"#\"\"\"!\"\"" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>-%\"CG6#%\"xG,&\"%+I\"\"\"*&\"#?F*F'F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"PG6#%\"xG,(F'\"$!)**$)F'\"\"#\"\"\"!\" \"\"%+IF." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 86 "This is a parabola o pening down, with vertex at x = 490. The max. profit therefore is:" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "P := x -> 980*x-x^2-3000;\n P(490);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"PGf*6#%\"xG6\"6$%)opera torG%&arrowGF(,(9$\"$!)**$)F-\"\"#\"\"\"!\"\"\"%+IF3F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"'+rB" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 281 70 "7. Farmer wa nts to enclose a retangular garden, one side being a barn." }{TEXT -1 65 " He has 40ft of fence. What's the max. area that can be enclosed? " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "2*x + y = 40;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&%\"xG\"\"#%\"yG\"\"\"\"#S" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 12 "solve(%, y);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#,&%\"xG!\"#\"#S\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 " A := (-2*x+40) * x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG*&,&%\"xG !\"#\"#S\"\"\"F*F'F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "exp and(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"xG\"\"#\"\"\"!\"#*& \"#SF(F&F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 139 "Once again, this is a parabola going down, so the max. is at the vertex, which is x = \+ 10. Then y = 20 and the max. area is 200 square feet." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 282 59 "11. What is the max. product of two numb ers that add to 18?" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 161 "If x, y are those numbers, then we know that x + y = 18 (or y = 18 - x). We want to find the max. product, i.e. P = x * (18 - x), which is a p arabola going down:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "P := x * (18 - x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"PG*&%\"xG\"\"\",&\"#=F'F &!\"\"F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expand(%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"xG\"#=*$)F$\"\"#\"\"\"!\"\"" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 83 "Thus, the vertex is a maximum, and is x = 9, so that the other number is 9 as well." }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 32 "P. 612 - (Log and Exp functions)" }}{EXCHG {PARA 0 "" 0 "" {TEXT 283 25 "7. Graph f(x) = 3^x + 1. " }{TEXT -1 49 "It's a standard exp. function, shifted up by one." }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 28 "plot(3^x+1, x=-4..2,-1..10);" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6% -%'CURVESG6$7W7$$!\"%\"\"!$\"3tXB,zcM75!#<7$$!3!******\\2<#pQF-$\"3%Q5 cGE`U,\"F-7$$!3#)***\\7bBav$F-$\"3r&zNWI^h,\"F-7$$!36++]K3XFOF-$\"3NcW XJ%*e=5F-7$$!3%)****\\F)H')\\$F-$\"3))Q\"Rcb:9-\"F-7$$!3#****\\i3@/P$F -$\"3g$e5?uaY-\"F-7$$!3;++Dr^b^KF-$\"3Q1x\">-%4G5F-7$$!3$****\\7Sw%GJF -$\"3+>y!Geh@.\"F-7$$!3*****\\7;)=,IF-$\"3.O[2B())p.\"F-7$$!3!)***\\i8 3V(GF-$\"3j+xE'H@D/\"F-7$$!3:+++NkzVFF-$\"3oW:k=o2\\5F-7$$!3w****\\d;% )GEF-$\"3/4jtYJob5F-7$$!37+++0)H%*\\#F-$\"3#4@ovA!>k5F-7$$!3#)*****\\d '[pBF-$\"3K#4[:?SS2\"F-7$$!38+++&>iUC#F-$\"3S=I0f+'\\3\"F-7$$!3!)***\\ 7YY08#F-$\"3/w\"oFdli4\"F-7$$!3)******\\XF`*>F-$\"3*pdKf%Ho66F-7$$!3)* ******>#z2)=F-$\"3y+)GgAgm7\"F-7$$!3/++D\"RKvu\"F-$\"3_T\"\\kSFm9\"F-7 $$!3<+++qjeH;F-$\"39CBbCG\"p;\"F-7$$!3()***\\7*3=+:F-$\"3c-'[![=T#>\"F -7$$!3%)***\\PFcpP\"F-$\"3')eyXu_I?7F-7$$!3#)****\\7VQ[7F-$\"3[M&[T`GP D\"F-7$$!3\")***\\i6:.8\"F-$\"3I0@wF,())G\"F-7$$!31++]P:'H+\"F-$\"3S%f c&o0DK8F-7$$!3[++]7'pnq)!#=$\"3O[&G'p8A%Q\"F-7$$!3'3++v[G_b(Fcs$\"3[-G 1]w.O9F-7$$!3t)****\\_K:J'Fcs$\"3gvjtXs()*\\\"F-7$$!36-+++HnE]Fcs$\"3W 9f\"f#4mv:F-7$$!3y,++D%)opPFcs$\"3!>\")*Q(p14m\"F-7$$!3G++]78\\`DFcs$ \"3K-\\t8NQbfjs\\JJ#F-7$$\"3W.++]&*=jPFcs$\"3R:4AqH*>^#F-7$$\"3#f*** \\(3/3(\\Fcs$\"3'=tJo:/ls#F-7$$\"3z++]P#4JB'Fcs$\"3]s-0%eHL)HF-7$$\"3W (*****\\KCnuFcs$\"35Tm+X&=8F$F-7$$\"3A(***\\(=n#f()Fcs$\"3c-wd&Q?xh$F- 7$$\"3P+++!)RO+5F-$\"3#z'>ee)*>,SF-7$$\"30++]_!>w7\"F-$\"3cy2Z]\\_^WF- 7$$\"3O++v)Q?QD\"F-$\"3y?Fs[!G['\\F-7$$\"3G+++5jyp8F-$\"3u4\\(eVTN]&F- 7$$\"3<++]Ujp-:F-$\"3S9\\_nuc6iF-7$$\"33++D,X8i:F-$\"3=85eZrBjlF-7$$\" 3++++gEd@;F-$\"3zB-aKqjQpF-7$$\"31+]PMh%\\o\"F-$\"3#pJ#ou_$oO(F-7$$\"3 9++v3'>$[F-$\"3%)=Lo$RJ!y$*F-7$$\"\" #F*$\"#5F*-%'COLOURG6&%$RGBG$F]\\l!\"\"$F*F*Fd\\l-%+AXESLABELSG6$Q\"x6 \"Q!Fi\\l-%%VIEWG6$;F(Fj[l;$Fc\\lF*F\\\\l" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 1 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 284 22 "9. Graph y = log_5(x)." }{TEXT -1 36 " It's a standard logarithm function." }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "plot(log[5](x),x=0..10);" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$7^o7$$\"3S+++v1h6o!#?$!3k,xS$p=**4$!#<7$$\" 33+++N@Ki8!#>$!3K3VLN@CpEF-7$$\"3<+++-K[V?F1$!3!\\ut!*\\7tT#F-7$$\"3;+ ++qUkCFF1$!3)e\"4ExbcQAF-7$$\"32+++P`!eS$F1$!3Y=*)\\$p=**4#F-7$$\"3s** ***\\Smp3%F1$!3=B$[3%fj')>F-7$$\"3)******>ZF\"oZF1$!37*o]$Qn&3*=F-7$$ \"3K+++S&)G\\aF1$!3aAv=>!*)y!=F-7$$\"3B+++v1h6oF1$!3w3VLN@Cp;F-7$$\"3W ******4G$R<)F1$!3_I\\x#Qffb\"F-7$$\"3/+++X\\DO&*F1$!3-T@@!=!=g9F-7$$\" 31+++3x&)*3\"!#=$!3UHT6hC@x8F-7$$\"3/+++N@Ki8F^o$!3V:4ExbcQ7F-7$$\"3*) *****>c'yM;F^o$!3SP:qCGGD6F-7$$\"3,+++*)4D2>F^o$!3\"zuQ@i.&H5F-7$$\"3' )*****fT:(z@F^o$!3EktSI!f`Y*F^o7$$\"3?+++!y%*z7$F^o$!3$=exwt56A(F^o7$$ \"33+++XTFwSF^o$!3M8JN*Rqed&F^o7$$\"3t*****zY8F9&F^o$!3kaE:kO!>8%F^o7$ $\"3&******4z_\"4iF^o$!3W1bs'pP5'HF^o7$$\"3e*****f;hEG(F^o$!3_[&3Z>$=q >F^o7$$\"3C+++S&phN)F^o$!3if>.$4Ce6\"F^o7$$\"3%*******)=)H\\5F-$\"3%) \\p^m*f**)HF17$$\"31+++[!3uC\"F-$\"35****y*prNP\"F^o7$$\"35+++J$RDX\"F -$\"3/`^qqe_>BF^o7$$\"3'******zR'ok;F-$\"3YF>F07bmJF^o7$$\"31+++1J:w=F -$\"3vp=/v^e4RF^o7$$\"3))*****zgsO4#F-$\"3)H^Y5cm6f%F^o7$$\"3!)*****R! RE&G#F-$\"3v#4)Hg$=_8&F^o7$$\"3\")*****\\K]4]#F-$\"3%esb4&ef&p&F^o7$$ \"3;+++vB_0)4IiHhqF^o7$$\"3;+++347TLF-$\"3?;92#y-_\\(F^o7$$\" 3()*****HjM?`$F-$\"3&G\"p0SXYSyF^o7$$\"31+++\"o7Tv$F-$\"3hCwZA8M>#)F^o 7$$\"3%)*****HQ*o]RF-$\"3u*f,!)4fk`)F^o7$$\"3u*****4=lj;%F-$\"3e)zb:)G sm))F^o7$$\"3M+++V&RY2aF -$\"3)zr(=uln[5F-7$$\"3#)*****zdWZh&F-$\"3AEqfr)[?2\"F-7$$\"3,+++\\y)) GeF-$\"3WqeB8bI&4\"F-7$$\"3D+++i_QQgF-$\"3qMHt3^C<6F-7$$\"3c******zZ3T iF-$\"3W5$4r&*fx8\"F-7$$\"3))*****f.[hY'F-$\"391r_=o!R1()>\"F-7$$\"3O+++(pe *zqF-$\"3)p(=jI!>h@\"F-7$$\"3=+++C\\'QH(F-$\"3e/kJvLhM7F-7$$\"3Q+++8S8 &\\(F-$\"3]F`b%QE:D\"F-7$$\"3t*****\\?=bq(F-$\"37_fl>mso7F-7$$\"3N+++2 s?6zF-$\"3epT]f[4&G\"F-7$$\"3K+++IXaE\")F-$\"399w+p5y,8F-7$$\"3y+++l*R RL)F-$\"3'fUTW.RuJ\"F-7$$\"3S*****HvJga)F-$\"3:OH#3j`IL\"F-7$$\"3;+++8 tOc()F-$\"3%>^ub\"3;[8F-7$$\"3?******[Qk\\*)F-$\"3UMV`yhsh8F-7$$\"3a** ****o0;r\"*F-$\"31R.'3)y\"pP\"F-7$$\"3E*****\\w(Gp$*F-$\"3%e3fB#y>!R\" F-7$$\"3C******zE`!e*F-$\"3Isx2w60/9F-7$$\"33+++<5s#y*F-$\"3sE%p%Hu-<9 F-7$$\"#5\"\"!$\"3L$Rt!elnI9F--%'COLOURG6&%$RGBG$F\\`l!\"\"$F]`lF]`lFf `l-%+AXESLABELSG6$Q\"x6\"Q!F[al-%%VIEWG6$;Ff`lF[`l%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 1 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 285 24 "40.Graph f(x) = e^x - 1." }{TEXT -1 100 " Standard exp. functi on, shifted down by 1. Domain is all numbers, range all numbers bigger than -1." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "plot(exp(x)-1, x = -4. .2);" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$7V7$$!\"%\"\"!$!3!yl76hVo\")*!# =7$$!3!******\\2<#pQ!#<$!3U2WTOHD\"z*F-7$$!3#)***\\7bBav$F1$!3+iUC#F1$!3&zz#>pF%* R*)F-7$$!3!)***\\7YY08#F1$!3roP$QGwA\"))F-7$$!3)******\\XF`*>F1$!3?!>H *o(3.k)F-7$$!3)*******>#z2)=F1$!3AMB#>\\(Gv%)F-7$$!3/++D\"RKvu\"F1$!3a i)y%4s'zD)F-7$$!3<+++qjeH;F1$!3#yf-wm$*)R!)F-7$$!3()***\\7*3=+:F1$!3o# zZ\\)>5pxF-7$$!3%)***\\PFcpP\"F1$!3E5PlTaawuF-7$$!3#)****\\7VQ[7F1$!3F +pmn#>.8(F-7$$!3\")***\\i6:.8\"F1$!3_>]p0_oqnF-7$$!31++]P:'H+\"F1$!3t[ d**eV3KjF-7$$!3[++]7'pnq)F-$!3ZelS(o>L\"eF-7$$!3'3++v[G_b(F-$!34LY*\\l ]BI&F-7$$!3t)****\\_K:J'F-$!3=_'Ryd?-o%F-7$$!36-+++HnE]F-$!3m3&f!y(\\3 &RF-7$$!3y,++D%)opPF-$!3tR'4MaD19$F-7$$!3G++]78\\`DF-$!3!z)o\"Q-SND#F- 7$$!3)3++]x6J?\"F-$!3YGgI+^bL6F-7$$\"3_y&******Hk-\"!#?$\"3wQAbfp&p-\" Fgu7$$\"30,++]A!eI\"F-$\"39#)**fa32%*4,9F17$$\"3P+++!)RO+ 5F1$\"3liw7\"F1$\"3[Q21sYH)3#F17$$\"3O++v)Q?QD\" F1$\"3o&)=KGHq.DF17$$\"3G+++5jyp8F1$\"3rOZAS)4X$HF17$$\"3<++]Ujp-:F1$ \"3EI9BX&*y$\\$F17$$\"3++++gEd@;F1$\"3m-*f;OV51%F17$$\"31+]PMh%\\o\"F1 $\"3AFFVs/;#R%F17$$\"39++v3'>$[/^F17$$\"37++D6Ejp=F1$\"3a!f1+68f[&F17$$\"31+]i0j\"[$>F1$ \"3/nqCkAxAfF17$$\"\"#F*$\"3S]1$*)4c!*Q'F1-%'COLOURG6&%$RGBG$\"#5!\"\" $F*F*F`\\l-%+AXESLABELSG6$Q\"x6\"Q!Fe\\l-%%VIEWG6$;F(Fe[l%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 1 "Curve 1" }}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 286 29 "41. Graph g(x) = 0.6 * ln(x)." }{TEXT -1 85 " It's a sta ndard log. function. Domain is all positive numbers, range is all numb ers:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "plot(0.6*ln(x),x=0..10);" } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$7^o7$$\"3S+++v1h6o!#?$!3!37!Q-gZ$*H!#<7 $$\"33+++N@Ki8!#>$!3c`T/%p(exDF-7$$\"3<+++-K[V?F1$!3JjgKH'3VL#F-7$$\"3 ;+++qUkCFF1$!3w'=3dQ*ph@F-7$$\"32+++P`!eS$F1$!3nXx+bK\"y-#F-7$$\"3s*** **\\Smp3%F1$!3&zGV3K?%=>F-7$$\"3)******>ZF\"oZF1$!3v])4I\"*Hf#=F-7$$\" 3K+++S&)G\\aF1$!3_>APx5\"eu\"F-7$$\"3B+++v1h6oF1$!3z$p$eY\\#>h\"F-7$$ \"3W******4G$R<)F1$!3;@t]7?`-:F-7$$\"3/+++X\\DO&*F1$!31m4h/;/59F-7$$\" 31+++3x&)*3\"!#=$!3G_i.pF#*H8F-7$$\"3/+++N@Ki8F^o$!3aExCQm.'>\"F-7$$\" 3*)*****>c'yM;F^o$!3#RNrTqVm3\"F-7$$\"3,+++*)4D2>F^o$!35()*\\F'H`T**F^ o7$$\"3')*****fT:(z@F^o$!3n_G+2YMS\"*F^o7$$\"3?+++!y%*z7$F^o$!3#R'>mMw :tpF^o7$$\"33+++XTFwSF^o$!3u!yA$H.T%Q&F^o7$$\"3t*****zY8F9&F^o$!3y%fnX WD+*RF^o7$$\"3&******4z_\"4iF^o$!3WXRb(zj$fGF^o7$$\"3e*****f;hEG(F^o$! 3#Qo-o^KD!>F^o7$$\"3C+++S&phN)F^o$!3==)f$f(4v2\"F^o7$$\"3%*******)=)H \\5F-$\"3EVN1cHH()GF17$$\"31+++[!3uC\"F-$\"3#[9`9-2kK\"F^o7$$\"35+++J$ RDX\"F-$\"36a26D(z)RAF^o7$$\"3'******zR'ok;F-$\"3'47do`?y0$F^o7$$\"31+ ++1J:w=F-$\"3!ehh:wS`x$F^o7$$\"3))*****zgsO4#F-$\"3'zw)Q:&=NV%F^o7$$\" 3!)*****R!RE&G#F-$\"3ua[hq!*))e\\F^o7$$\"3\")*****\\K]4]#F-$\"3[/$eytC +]&F^o7$$\"3;+++vB_Y2aF-$\"3'[`F=!zm75F-7$$\"3#)*****zdWZh&F-$\"3Mq#e(ewBN5F-7 $$\"3,+++\\y))GeF-$\"3)*R*>7t&pd5F-7$$\"3D+++i_QQgF-$\"3O1eG\")>))y5F- 7$$\"3c******zZ3TiF-$\"3%>nKhS#p)4\"F-7$$\"3))*****f.[hY'F-$\"3eC)RTM[ *>6F-7$$\"31+++#Qx$omF-$\"3f:2cNfUQ6F-7$$\"3Q+++u.I%)oF-$\"3UiVi1had6F -7$$\"3O+++(pe*zqF-$\"3sH*eV%3Ou6F-7$$\"3=+++C\\'QH(F-$\"3]r%fS9?A>\"F -7$$\"3Q+++8S8&\\(F-$\"3%R&*GqS_&37F-7$$\"3t*****\\?=bq(F-$\"3'*)=8L.i ^A\"F-7$$\"3N+++2s?6zF-$\"3Y5hxK#o4C\"F-7$$\"3K+++IXaE\")F-$\"3e2**o$[ \"3d7F-7$$\"3y+++l*RRL)F-$\"3Cj.h(z,AF\"F-7$$\"3S*****HvJga)F-$\"3S=El J-G(G\"F-7$$\"3;+++8tOc()F-$\"3zNmi\"*ReN\"F-7$$\"33+++< 5s#y*F-$\"35!Go2gq$o8F-7$$\"#5\"\"!$\"3WFkzb5b\"Q\"F--%'COLOURG6&%$RGB G$F\\`l!\"\"$F]`lF]`lFf`l-%+AXESLABELSG6$Q\"x6\"Q!F[al-%%VIEWG6$;Ff`lF [`l%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 1 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 288 20 "43. Solve 3^x = 1/9." }{TEXT -1 57 " Sin ce 1/9 = 3^(-2), we have 3^x = 3^(-2), so that x = -2" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "evalf(solve(3^x = 1/9, x));" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+********>!\"*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 287 18 "45. log_x(32) = 5." }{TEXT -1 100 " We need to raise thi s to the exp. function base x on both sides, which gives 32 = x^5. Hen ce x = 2." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "solve(log[x](32) = 5, \+ x);" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 289 18 "47. 3*ln(x) = -6. " }{TEXT -1 106 "First we di vide by 3: ln(x) = -2. We then apply the exponential function on both \+ sides, getting x = e^(-2)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "solve( 3*ln(x) = -6, x);" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$expG6#!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 290 23 "53. log_3(2*x - 5) = 1. " }{TEXT -1 81 " We apply the exp. function base 3 on both sides, so 2 *x - 5 = 3. But then x = 4." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "solv e(log[3](2*x-5)=1);" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 291 30 "54. lo g_4(x) + log_4(x-6) = 2." }}{PARA 0 "" 0 "" {TEXT -1 313 " We apply th e rules of logs to combine into a single log: log_4(x * (x-6)) = 2. Th en we apply the ep. function base 4 on both sides: x*(x-6) = 4^2 = 16. Now it's a simple quadratic equation: x^2 - 6*x - 16 = 0. Because the domain of logs is all positive numbers, the solution is only the posi tive one, i.e. x = 8." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "solve(x^2 \+ - 6*x - 16 = 0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\")!\"#" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 292 27 "55. log(x) + log(x-15) = 2." } {TEXT -1 192 " It's the natural log (base 10). We apply the rules of l og: log(x * (x-15) ) = 2. Then we apply 10^(...) on both sides, so: x* (x-15) = 10^2 = 100. Thus (again, only the positive number works):" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "solve(x*(x-15) = 100);" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"#?!\"&" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 293 33 "56. log_3(x-4) = 3 - log_x(x+4). " }{TEXT -1 248 "First \+ we move the logs to the same side: log_3(x-4) + log(x+4) = 3. Then we \+ combine, using prop. of logs: log_3((x-4) * (x+4)) = 3. Finally, we ap py 3^(...) on both sides: (x-4)*(x+4) = 27, or x^2 - 16 = 27. But then x^2 = 43, so that x = sqrt(43)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 32 "P. 614 - (Log and Exp functions) " }}{EXCHG {PARA 0 "" 0 "" {TEXT 294 53 "28. Graph f(x) = e^x + 3 and \+ state domain and range. " }{TEXT -1 111 "It's the regular exp. functio n, shifted up by three. Domain is all numbers, range is all numbers bi gger than 3:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "plot(exp(x) + 3, x= -4..2,-1..10);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 " 6%-%'CURVESG6$7V7$$!\"%\"\"!$\"3AM()))QcJ=I!#<7$$!3!******\\2<#pQF-$\" 3Ef&ejqu3-$F-7$$!3#)***\\7bBav$F-$\"3>yxTT0RBIF-7$$!36++]K3XFOF-$\"3#3 8K['QeEIF-7$$!3%)****\\F)H')\\$F-$\"3#zZ0uyQ-.$F-7$$!3#****\\i3@/P$F-$ \"3*G\\)Qf^PMIF-7$$!3;++Dr^b^KF-$\"3G\"*H;aRrQIF-7$$!3$****\\7Sw%GJF-$ \"38,?ScWyVIF-7$$!3*****\\7;)=,IF-$\"37U9V[zs\\IF-7$$!3!)***\\i83V(GF- $\"3#)R7H&=bk0$F-7$$!3:+++NkzVFF-$\"3)Ha.XnDV1$F-7$$!3w****\\d;%)GEF-$ \"3K\"\\f@+i@2$F-7$$!37+++0)H%*\\#F-$\"3;fgU;=8#3$F-7$$!3#)*****\\d'[p BF-$\"3/hI%RtGN4$F-7$$!38+++&>iUC#F-$\"3K?23Bd+1JF-7$$!3!)***\\7YY08#F -$\"38BmhrBx=JF-7$$!3)******\\XF`*>F-$\"3w!32J7pf8$F-7$$!3)*******>#z2 )=F-$\"3!ow23DrC:$F-7$$!3/++D\"RKvu\"F-$\"3u8@0zK?uJF-7$$!3<+++qjeH;F- $\"3)*R(RKj5g>$F-7$$!3()***\\7*3=+:F-$\"3t?_],)*3BKF-7$$!3%)***\\PFcpP \"F-$\"3?HY$eXXBD$F-7$$!3#)****\\7VQ[7F-$\"3)*4LBt!opG$F-7$$!3\")***\\ i6:.8\"F-$\"30)\\I%z9$HK$F-7$$!31++]P:'H+\"F-$\"37D/5k:zmLF-7$$!3[++]7 'pnq)!#=$\"3EW$f7.o'=MF-7$$!3'3++v[G_b(Fcs$\"3eO0]M\\wpMF-7$$!3t)**** \\_K:J'Fcs$\"3*[.;A%z(>`$F-7$$!36-+++HnE]Fcs$\"3O\\S>A]\"\\g$F-7$$!3y, ++D%)opPFcs$\"3!f.fcWPfo$F-7$$!3G++]78\\`DFcs$\"356$=w*fkuPF-7$$!3)3++ ]x6J?\"Fcs$\"3/(Rp**[Wm)QF-7$$\"3_y&******Hk-\"!#?$\"3-_&fp&p-,SF-7$$ \"30,++]A!eI\"Fcs$\"3A)**fa32%*4,aF-7$$\"3P+++!)RO+5F- $\"35jdF-7$$\"30++]_!>w7\"F-$\"3%*Q21sYH)3'F-7$$\"3O++v)Q?QD\"F- $\"3o&)=KGHq.lF-7$$\"3G+++5jyp8F-$\"3EOZAS)4X$pF-7$$\"3<++]Ujp-:F-$\"3 EI9BX&*y$\\(F-7$$\"3++++gEd@;F-$\"3w,*f;OV51)F-7$$\"31+]PMh%\\o\"F-$\" 35GFVs/;#R)F-7$$\"39++v3'>$[/\"*F-7$$\"37++D6Ejp=F-$\"3a!f1+68f[*F-7$$\"31+]i0j\"[$>F-$ \"3/nqCkAxA**F-7$$\"\"#F*$\"3/lI*)4c!*Q5!#;-%'COLOURG6&%$RGBG$\"#5!\" \"$F*F*Fa\\l-%+AXESLABELSG6$Q\"x6\"Q!Ff\\l-%%VIEWG6$;F(Fe[l;$F`\\lF*$F _\\lF*" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 1 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " " 0 "" {TEXT 295 54 "29. Graph g(x) = ln(x - 4) and state domain and r ange." }{TEXT -1 118 " It's the regular log. function, shifted to the \+ right by 4. Domain is all numbers bigger than 4, range is all numbers: " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plot(ln(x-4),x=0..14);" }} {PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$7T7$ $\"3.++++@T0S!#<$!31%z'Q\"4=\">_F*7$$\"3%)*****R/VX,%F*$!3n'f!GvCkIUF* 7$$\"3t******))RnBSF*$!3c7`4W$yLu$F*7$$\"3M+++K\\!G.%F*$!3*==U!4k</%F*$!3a1iWlNhrJF*7$$\"3/+++@o1^SF*$!3E5^:)G?Y(HF*7$$\"3 %******fw(>gSF*$!3t$\\!*p.?,\"GF*7$$\"3i*****\\lf%ySF*$!3qWaNN2fL#F*7$$\"3?+++L')))HTF*$!3R2\"3\\'y2T?F*7$ $\"3=+++Ad0jTF*$!3:zH$QGjO\"=F*7$$\"3;+++6GA'>%F*$!3l+FfuW]G;F*7$$\"3B +++,**QHUF*$!3-*f&z)4KBZ\"F*7$$\"3?+++zSs&H%F*$!3=*4N\\UG$=7F*7$$\"3C+ ++e#e?O%F*$!3&o9.k9]f,\"F*7$$\"3K+++lP\")>XF*$!3)[%R'yvYGa'!#=7$$\"3Q+ ++s#pvn%F*$!3-@jg\\[V#*QFbp7$$\"3p******z)37\"[F*$!3g7$$\"3A+++axvb_F*$\"3U>*[Uy\"RxAFbp 7$$\"3#******p8l4`&F*$\"3[q-D]M)*eUFbp7$$\"3))*****RD6H$eF*$\"3+>at>b0 fgFbp7$$\"3F+++i`V?hF*$\"3$G@X.F9i^(Fbp7$$\"3\"******\\gO/U'F*$\"3m,( \\=Rz%R))Fbp7$$\"3u*****fRJfp'F*$\"3!\\`(QhuV<**Fbp7$$\"3'******pu*3$* pF*$\"3uXT09iI'4\"F*7$$\"3E+++ePv,tF*$\"3KDa7pPX%>\"F*7$$\"3c*****poY/ d(F*$\"3ObLP52ps7F*7$$\"3!)*****>TU1'yF*$\"3E9%3wfL3N\"F*7$$\"3/+++\"* HWg\")F*$\"3ed[#ob@cU\"F*7$$\"3!3++!o$RPX)F*$\"3KjKt]Su$\\\"F*7$$\"3M+ ++&p=vt)F*$\"3A,\\d;N^b:F*7$$\"3y*****RD2E0*F*$\"3!pIxzR/*>;F*7$$\"37* ****zLGdL*F*$\"3k*)y9'RDWn\"F*7$$\"3.+++E0-Q'*F*$\"3X2!QL.L&H\"**F*$\"3WA::.W(px\"F*7$$\"31+++!4T6-\"!#;$\"3/[u?o!)QE=F*7$$ \"31+++i(=$\\5F[w$\"3CVF%)oNvq=F*7$$\"3)*******[Dxy5F[w$\"3)e.rg!f6:>F *7$$\"3-+++4!pv5\"F[w$\"3iv_*z(\\mc>F*7$$\"33+++NirP6F[w$\"3]j6Df!*Q)* >F*7$$\"3/+++&f^n;\"F[w$\"3wyF@(p#*p.#F*7$$\"3%******fWWk>\"F[w$\"3Q!e $G$>()\\2#F*7$$\"3$******RU\"*eA\"F[w$\"3;g4&48$H6@F*7$$\"3-+++R,&HD\" F[w$\"3;bA514`V@F*7$$\"3%*******zC'RG\"F[w$\"3%)*))4BVW#z@F*7$$\"3.+++ (G+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 300 2 "33" }{TEXT -1 2 ". " }{TEXT 296 16 "Solve log(x) = 4" }{TEXT -1 61 ". This is the common log (base 10), so that x = 10^4 = 10,000" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 299 2 "34" }{TEXT -1 2 ". " }{TEXT 297 23 "Solve 5^(4-3*x) = 125. " }{TEXT -1 73 "Since \+ 125 = 5^3 we have 5^(4-3*x) = 5^3, so that 4 - 3*x = 3, or x = 1/3." } }}{EXCHG {PARA 0 "" 0 "" {TEXT 298 41 "37. Solve log(x-3) + log(x + 1) = log(5)." }{TEXT -1 162 " This is equivalent to log( (x-3) * (x+1)) \+ = log(5). Applying the exp. function base 10 on both sides gives: (x-3 )*(x+1)=5, which is a regular quadratic equation:" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 14 "(x-3)*(x+1)=5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/ *&,&%\"xG\"\"\"\"\"$!\"\"F',&F&F'F'F'F'\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expand(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/, (*$)%\"xG\"\"#\"\"\"F)*&F(F)F'F)!\"\"\"\"$F+\"\"&" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 12 "solve(%, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"%!\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 94 "It can't be -2 , because that's not in the domain of log(x+1), so the single solution is x = 4." }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{MARK "6 5 0 1" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }