{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 "" -1 259 "" 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 }{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 "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 }{PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 68 "1.\011State, in your own \+ words, the definition of the following terms:\n" }{TEXT -1 55 "a)\011s lope of a line through two points (x, y) and (x, y)" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 75 "If P1 = (x1, y1) and P2 = (x2, y2) then the slope m = (y2 - y1) / (x2 - x1)" }}{PARA 0 "" 0 " " {TEXT -1 13 "\nb)\011function\n" }}{PARA 0 "" 0 "" {TEXT -1 91 "A fu nction is a rule that assigns to every number in its domain exactly on e outcome number." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 20 "c)\011range and domain\n" }}{PARA 0 "" 0 "" {TEXT -1 52 " Domain: All numbers for which a function is defined." }}{PARA 0 "" 0 " " {TEXT -1 50 "Range: All possible outcome numbers of a function." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 19 "d)\011lin ear function\n" }}{PARA 0 "" 0 "" {TEXT -1 67 "A function with two var iables, each raised to a power of at most 1." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 12 "e)\011monomial\n" }}{PARA 0 "" 0 "" {TEXT -1 51 "Products of integer powers of variables and numbers " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 14 "f) \011polynomial\n" }}{PARA 0 "" 0 "" {TEXT -1 17 "Sums of monomials" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 257 120 "2.\011Find the slope and y-int ercept of the following lines, if possible, and graph them in the coor dinate system provided:" }}{PARA 0 "" 0 "" {TEXT -1 3 "2a)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 18 "f(x) := -3/5*x+12;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"fG6#%\"xG,&F'#!\"$\"\"&\"#7\"\"\"" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "Has slope -3/5, y-intercept 12. Th e graph is:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "plot(-3/5*x+ 12, x=-3..3);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6 %-%'CURVESG6$7S7$$!\"$\"\"!$\"33++++++!Q\"!#;7$$!3!******\\2<#pG!#<$\" 3/++]CI:s8F-7$$!3#)***\\7bBav#F1$\"3)***\\28aKl8F-7$$!36++]K3XFEF1$\"3 5++&*\\qkd8F-7$$!3%)****\\F)H')\\#F1$\"3#****\\'*y<*\\8F-7$$!3#****\\i 3@/P#F1$\"3,+]p@G\"F-7$$!3\"******\\>iUC\"F 1$\"31++qJdlu7F-7$$!3-++DhkaI6F1$\"3-+]n(yKyE\"F-7$$!3s******\\XF`**!# =$\"3/++IZ'>(f7F-7$$!3u*******>#z2))Fgp$\"31++?`n%GD\"F-7$$!3S++]7RKvu Fgp$\"31+]ZV>&[C\"F-7$$!3s,+++P'eH'Fgp$\"30++?#=vxB\"F-7$$!3q)***\\7*3 =+&Fgp$\"31+]Z`3,I7F-7$$!3[)***\\PFcpPFgp$\"3&***\\UwthA7F-7$$!3;)**** \\7VQ[#Fgp$\"3/++veI!\\@\"F-7$$!32)***\\i6:.8Fgp$\"3'***\\(p!*=y?\"F-7 $$!3Wb+++v`hH!#?$\"3&****\\Apx,?\"F-7$$\"3]****\\(QIKH\"Fgp$\"3++]n<1C #>\"F-7$$\"38****\\7:xWCFgp$\"3#***\\#4PJ`=\"F-7$$\"3E,++vuY)o$Fgp$\"3 3++:&>py<\"F-7$$\"3!z******4FL(\\Fgp$\"3+++SP+;q6F-7$$\"3A)****\\d6.B' Fgp$\"3%****\\08=E;\"F-7$$\"3s****\\(o3lW(Fgp$\"3/+](y%4Kb6F-7$$\"35** ***\\A))oz)Fgp$\"31++lq'=s9\"F-7$$\"3e******Hk-,5F1$\"31++?9%Q*R6F-7$$ \"36+++D-eI6F1$\"3)*****\\'=l@8\"F-7$$\"3u***\\(=_(zC\"F1$\"34+](o[@^7 \"F-7$$\"3M+++b*=jP\"F1$\"30++qi3U<6F-7$$\"3g***\\(3/3(\\\"F1$\"3&*** \\Zv^<56F-7$$\"33++vB4JB;F1$\"3%***\\dW8g-6F-7$$\"3u*****\\KCnu\"F1$\" 3#*****\\Sl>&4\"F-7$$\"3s***\\(=n#f(=F1$\"31+](oRWu3\"F-7$$\"3P+++!)RO +?F1$\"3/++?h\"y*z5F-7$$\"30++]_!>w7#F1$\"3%****\\o&GMs5F-7$$\"3O++v)Q ?QD#F1$\"3#***\\nw2xk5F-7$$\"3G+++5jypBF1$\"3'*****R@G\"y0\"F-7$$\"3<+ +]Ujp-DF1$\"3'****\\%>#Q)\\5F-7$$\"3++++gEd@EF1$\"3+++SScqU5F-7$$\"39+ +v3'>$[FF1$\"3#***\\ZB35N5F-7$$\"37++D6EjpGF1$\"30+]KV?#y-\"F-7$$\"\"$ F*$\"3$*************>5F--%'COLOURG6&%$RGBG$\"#5!\"\"$F*F*Fb[l-%+AXESLA BELSG6$Q\"x6\"Q!Fg[l-%%VIEWG6$;F(Fgz%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 " " {TEXT 259 5 "2. b)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "solve(-5*y \+ - 2*x = 7, y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"xG#!\"#\"\"&#\" \"(F'!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 46 "Slope is -2/5, y i ntercept -7/5. The graph is" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "plot(-2/5*x - 7/5, x = -5..5);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$7S7$$!\"&\"\"!$\"3)3+++++++'!#=7$$! 3YLLLe%G?y%!#<$\"3[OLLLQ6G^F-7$$!3OmmT&esBf%F1$\"3QmmmT.\\pVF-7$$!3ALL $3s%3zVF1$\"3AMLL$))Qj^$F-7$$!3_LL$e/$QkTF1$\"3SNLL$=Kvl#F-7$$!3ommT5= q]RF1$\"3]ommTs!G!=F-7$$!3ILL3_>f_PF1$\"3^MLL3yO55F-7$$!3K++vo1YZNF1$ \"3EE++]nU)*=!#>7$$!3;LL3-OJNLF1$!3K^mm;fX(e'FR7$$!3p***\\P*o%Q7$F1$!3 O+++DCh/:F-7$$!3Kmmm\"RFj!HF1$!3'HLLLV!puBF-7$$!33LL$e4OZr#F1$!3)emmmh b59$F-7$$!3u*****\\n\\!*\\#F1$!3X*******H,Q+%F-7$$!3%)*****\\ixCG#F1$! 3'))******\\*3q[F-7$$!3#******\\KqP2#F1$!3,*******p=\\q&F-7$$!39LL3-TC %)=F1$!3ilmm\"fBIY'F-7$$!3[mmm\"4z)e;F1$!3+LLLLO[ktF-7$$!3Mmmmm`'zY\"F 1$!3OLLLL&Q\"G\")F-7$$!3#****\\(=t)eC\"F1$!3A*****\\s]k,*F-7$$!3!ommmh 5$\\5F1$!3mJLLLvv-)*F-7$$!3S$***\\(=[jL)F-$!3A++]sgam5F17$$!3)f***\\iX g#G'F-$!3;++]<#F-$ !3BLL$eDBJJ\"F17$$!3vDMLLe*e$\\!#?$!3ammmTc-)R\"F17$$\"3!=nm\"zRQb@F-$ !3qmm;f`@'[\"F17$$\"3_,+](=>Y2%F-$!3#*****\\nZ)Hc\"F17$$\"3summ\"zXu9' F-$!3#omm;$y*ek\"F17$$\"3#4+++]y))G)F-$!3++++S^bJF17$$\"3iKLL$Qx$o;F1$!3'HLLL&4Nn?F17$$\"3Y+++v.I%)=F1$! 3G+++],s`@F17$$\"3?mm\"zpe*z?F1$!3Smm;zM)>B#F17$$\"3;,++D\\'QH#F1$!3H+ ++qfa " 0 "" {MPLTEXT 1 0 20 "solve(y + 5 = 7, y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "slope is zero, y intercept 2. The \+ graph is:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "plot(2, x=-3.. 3);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVES G6$7S7$$!\"$\"\"!$\"\"#F*7$$!3!******\\2<#pG!#iUC\"F0F+7$$!3-++DhkaI6F0 F+7$$!3s******\\XF`**!#=F+7$$!3u*******>#z2))FhnF+7$$!3S++]7RKvuFhnF+7 $$!3s,+++P'eH'FhnF+7$$!3q)***\\7*3=+&FhnF+7$$!3[)***\\PFcpPFhnF+7$$!3; )****\\7VQ[#FhnF+7$$!32)***\\i6:.8FhnF+7$$!3Wb+++v`hH!#?F+7$$\"3]**** \\(QIKH\"FhnF+7$$\"38****\\7:xWCFhnF+7$$\"3E,++vuY)o$FhnF+7$$\"3!z**** **4FL(\\FhnF+7$$\"3A)****\\d6.B'FhnF+7$$\"3s****\\(o3lW(FhnF+7$$\"35** ***\\A))oz)FhnF+7$$\"3e******Hk-,5F0F+7$$\"36+++D-eI6F0F+7$$\"3u***\\( =_(zC\"F0F+7$$\"3M+++b*=jP\"F0F+7$$\"3g***\\(3/3(\\\"F0F+7$$\"33++vB4J B;F0F+7$$\"3u*****\\KCnu\"F0F+7$$\"3s***\\(=n#f(=F0F+7$$\"3P+++!)RO+?F 0F+7$$\"30++]_!>w7#F0F+7$$\"3O++v)Q?QD#F0F+7$$\"3G+++5jypBF0F+7$$\"3<+ +]Ujp-DF0F+7$$\"3++++gEd@EF0F+7$$\"39++v3'>$[FF0F+7$$\"37++D6EjpGF0F+7 $$\"\"$F*F+-%'COLOURG6&%$RGBG$\"#5!\"\"$F*F*Fau-%+AXESLABELSG6$Q\"x6\" Q!Ffu-%%VIEWG6$;F(Fht%(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 0 "" }{TEXT 261 5 "2. d)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "solve(3 = x - 1,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 46 "Vertical line (undefined slope) through x = 4." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 262 59 "3.\011Find the linear equation describing the following \+ lines\n" }{TEXT -1 41 "a)\011line with slope 4 containing (-2, -4)\n" }}{PARA 0 "" 0 "" {TEXT -1 17 "y + 4 = 4 (x + 2)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "3. b)\011line thr ough (3, -1) and (4, -2)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "m := (-2 - (-1)) / (4 - 3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"mG !\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "y +2 = m * (x - 4) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&%\"yG\"\"\"\"\"#F&*&%\"mGF&,&% \"xGF&\"\"%!\"\"F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "c)\011line containing (-3, 2) and \+ parallel to the line 2x - 5y = 8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "solve(2*x - 5*y = 8, y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"xG#\"\"#\"\"&#\"\")F'!\"\"" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 9 "m := 2/5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"mG#\"\"#\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "y - 2 = \+ m * (x + 3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&%\"yG\"\"\"\"\"#!\" \",&%\"xG#F'\"\"&#\"\"'F,F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "d)\011line containing (-3, 2) and perpendicular to the line 2x - 5y = 8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "m := -1 / (2/5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"mG#!\"&\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "y - 2 = m * (x + 3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&%\"yG\"\"\" \"\"#!\"\",&%\"xG#!\"&F'#\"#:F'F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 80 "e)\011line th rough (1, 2) and perpendicular to the line through (-2, -2) and (3, 1) " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "m := (1 - (-2)) / (3 - \+ (-2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"mG#\"\"$\"\"&" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "m := -1 / (3/5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"mG#!\"&\"\"$" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 20 "y - 2 = m * (x - 1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/,&%\"yG\"\"\"\"\"#!\"\",&%\"xG#!\"&\"\"$#\"\"&F-F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "f)\011line through (-2, -2) and (3, -2)" }}{PARA 0 "" 0 "" {TEXT -1 82 "m = 0, so it's a horizontal line passin g through y = -2, so the equation is y = -2" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 37 "g)\011line through (-2, -2) and (-2, 3)\n" }}{PARA 0 "" 0 "" {TEXT -1 94 "m = 1/0 = undefined , so it's a vertical line passing through x = -2, so the equation is x = -2" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 263 85 "4.\011For the following problems, evaluate the given fun ction at the indicated position." }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 30 "f := x -> (x - 3) / (2*x - 5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arrowGF(*&,&9$\" \"\"\"\"$!\"\"F/,&F.\"\"#\"\"&F1F1F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "f(-1 );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"%\"\"(" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 7 "f(a+h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*& ,(%\"aG\"\"\"%\"hGF&\"\"$!\"\"F&,(F%\"\"#*&F+F&F'F&F&\"\"&F)F)" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "g := t -> 5*t^2 + 4*t;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGf*6#%\"tG6\"6$%)operatorG%&arrow GF(,&*$)9$\"\"#\"\"\"\"\"&*&\"\"%F1F/F1F1F(F(F(" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 5 "g(0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"! " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "g(-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 " g(2*a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"aG\"\"#\"\"\"\"#?*& \"\")F(F&F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "(g(a+h) - \+ g(a-h)) / h;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,(*$),&%\"aG\"\"\"% \"hGF)\"\"#F)\"\"&*&\"\")F)F*F)F)*&F,F)),&F(F)F*!\"\"F+F)F2F)F*F2" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"aG\"#?\"\")\"\"\"" }}}{EXCHG {PARA 256 "" 0 " " {TEXT -1 160 "5.\011Which of the following graphs represent a functi ons, which ones not? For each graph representing a function, determine the range and domain of that function." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 115 "First is a function. Domain is all \+ numbers, range is all numbers (it's hard to see, but that's what it se ems like)." }}{PARA 0 "" 0 "" {TEXT -1 25 "Second is not a function." }}{PARA 0 "" 0 "" {TEXT -1 55 "Third is a function, domain is -1 to 1, range is 0 to 1" }}{PARA 0 "" 0 "" {TEXT -1 68 "Fourth is a function, domain is -1 to 2, range is the numbers \{1, 2\}" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 264 52 "6.\011Solve the \+ following systems of linear equations. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "solve( \{2* x-3*y=0, -4*x+3*y=-1\}, \{x,y\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#< $/%\"xG#\"\"\"\"\"#/%\"yG#F'\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "solve( \{2*x+y=6, 3*x+4*y=4\}, \{x, y\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%\"xG\"\"%/%\"yG!\"#" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 36 "solve( \{9*x-6*y=2, x=4*y+5\}, \{x,y\});" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%\"xG#!#6\"#:/%\"yG#!#V\"#I" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "solve( \{0.2*x+0.3*y=1.7, 1/ 7*x+1/5*y=-29/35\}, \{x,y\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/% \"xG$!$1#\"\"!/%\"yG$\"$V\"F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "solve( \{3*y-2*x=6, 8*x-12*y=-24\}, \{x,y\});" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#<$/%\"yG,&%\"xG#\"\"#\"\"$F)\"\"\"/F'F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 73 "This means there are infinitely many solu tions, or the lines are the same" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "solve( \{y=x+2, y-x=8\}, \{x ,y\});" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 79 "This means there are no solutions, or the lines are parallel but not identical." }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 265 79 "7.\011Sol ve the following inequalities and draw the solution set on a number li ne." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "solve(-4*y-3>=5, y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%*RealRangeG6$,$%)infinityG!\"\"!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "solve( -8*(2*x+3) + 6*(4-5*x) >= 2*(1-7*x)-4*(4+6*x), x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%*RealRangeG6$,$%)infinityG! \"\"#\"\"(\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "solve(-1 5 < -4*x-5, x);solve(-4*x-5<1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%* RealRangeG6$,$%)infinityG!\"\"-%%OpenG6##\"\"&\"\"#" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#-%*RealRangeG6$-%%OpenG6##!\"$\"\"#%)infinityG" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "This means that the answer is (-3/ 2, 5/2)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "solve(-1/3 <= 1/6*x-1);solve(1/6*x-1<1/4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%*RealRangeG6$\"\"%%)infinityG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%*RealRangeG6$,$%)infinityG!\"\"-%%OpenG6##\"# :\"\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "This means that the ans wer is (15/2, 4)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "solve(3*x-2 < 7);solve(x-2 > 4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%*RealRangeG6$,$%)infinityG!\"\"-%%OpenG6#\"\" $" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%*RealRangeG6$-%%OpenG6#\"\"'%)i nfinityG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 64 "This means that the a nswer is (-infinity, 3) union (6, infinity)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "solve(abs(4*x-1) \+ < 4.5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%*RealRangeG6$-%%OpenG6#$! ++++]()!#5-F'6#$\"++++v8!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "solve(abs(-5*t-3) > 10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$-%* RealRangeG6$-%%OpenG6##\"\"(\"\"&%)infinityG-F$6$,$F,!\"\"-F'6##!#8F+ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "solve(abs(2.1*x-7.9) < \+ -2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 89 "This means that there is \+ no answer (obviously, since an absolute value is never negative)" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 266 47 "8.\011Find the domains of the following functions:" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "f(x) := (x-2)/(3-x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"fG6 #%\"xG*&,&F'\"\"\"\"\"#!\"\"F*,&\"\"$F*F'F,F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "Domain is all numbers except 3." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "g(x) := sqr t(7-2*x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"gG6#%\"xG*$-%%sqrtG6 #,&\"\"(\"\"\"*&\"\"#F.F'F.!\"\"F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "solve(7-2*x >= 0, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%*RealRangeG6$,$%)infinityG!\"\"#\"\"(\"\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "That's the domain (-infinity, 7/2]." }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "h(x) := sqrt(2*x-4) / (x-4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"hG6#% \"xG*&,&F'\"\"#\"\"%!\"\"#\"\"\"F*,&F'F.F+F,F," }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 21 "solve(2*x-4 >= 0, x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%*RealRangeG6$\"\"#%)infinityG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 97 "Thus, the do main is all numbers bigger than or equal to 2, except 4 (because of th e denominator)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 267 36 "9.\011Perform the following operations " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "expand((4*x-1) * (4*x+1));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"xG\"\"#\"\"\"\"#;F(!\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "expand((a+b-1)*(a+b+1));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,**$)%\"aG\"\"#\"\"\"F(*(F'F(F&F(%\"bG F(F(*$)F*F'F(F(F(!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "e xpand((a^2+a-1)*(a^2+a*b+b^2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,4* $)%\"aG\"\"%\"\"\"F(*&)F&\"\"$F(%\"bGF(F(*&)F&\"\"#F()F,F/F(F(*$F*F(F( *&F.F(F,F(F(*&F&F(F0F(F(*$F.F(!\"\"*&F&F(F,F(F5*$F0F(F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "expand((x-2*y)*(x^2+1)*(3-2*y^2)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,2*$)%\"xG\"\"$\"\"\"F'*(\"\"#F(F% F()%\"yGF*F(!\"\"*&F'F(F&F(F(*(F*F(F&F(F+F(F-*(\"\"'F(F,F()F&F*F(F-*( \"\"%F()F,F'F(F2F(F(*&F1F(F,F(F-*&F4F(F5F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "factor(-2*x^3 + 4*x^2 - 2*x);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#,$*&%\"xG\"\"\"),&F%F&F&!\"\"\"\"#F&!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "factor(12*a^4-21*a^3-9*a^2);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&)%\"aG\"\"#\"\"\",(*$F%F(\"\"%*&\" \"(F(F&F(!\"\"\"\"$F.F(F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "factor( 5*x^2*(x-6) + 10*x*(6-x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(%\"xG\"\"\",&F%F&\"\"#!\"\"F&,&F%F&\"\"'F)F&\"\"&" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "f := x -> x^2;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arrowGF(*$)9$\" \"#\"\"\"F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 268 86 "10.\011If a given function f has a graph as indicated, please grap h the modified function" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 " plot(\{f(x), f(x)-2, f(x+1), f(x-2)+1, -f(x), f(-x)\}, x=-4..4);" }} {PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6)-%'CURVESG6$7S7$ $!\"%\"\"!$\"#;F*7$$!3ommmmFiDQ!#<$\"35KQGb*QNY\"!#;7$$!35LLLo!)*Qn$F0 $\"3eR.l,Fv\\8F37$$!3nmmmwxE.NF0$\"3#45.:^)GF7F37$$!3YmmmOk]JLF0$\"3*G 9bP^$*)46F37$$!3_LLL[9cgJF0$\"3O)*3po'[\"*)**F07$$!3smmmhN2-IF0$\"3b&) zlpcW7!*F07$$!3!******\\`oz$GF0$\"3[Y+l0a1a!)F07$$!3!omm;)3DoEF0$\"35X \\^nFc>rF07$$!3?+++:v2*\\#F0$\"39w&yfU)QXiF07$$!3BLLL8>1DBF0$\"3EgK$3! 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