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{SECT 0 {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 257 50 "High School Modul
es > Algebra by Gregory A. Moore " }}{PARA 3 "" 0 "" {TEXT -1 4 "    \+
" }{TEXT 256 44 "Intervals and Number Line Graphs [Algebra I]" }}
{PARA 0 "" 0 "" {TEXT -1 58 "\nThe number line graphs of finite and in
finite intervals.\n" }}{PARA 0 "" 0 "" {TEXT 258 153 "[Directions : Ex
ecute the Code Resource section first. Although there will be no outpu
t immediately, these definitions are used later in this worksheet.]" }
{TEXT -1 1 "\n" }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 5 "Code " }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "restart: with(plottools): with(plot
s):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1078 "intfin := proc( a,
 b, leq, req )\n          #description \"plot a finite interval on a n
umber line\";\nlocal r, M, v1, v2, wid, bar, Axesplot, leftpt, rightpt
, pt_color,\n      leftend, rightend, LT, RT, textpos;\n \nr := b-a ;
\nM := evalf( 1.2 * max( b-a, abs(a), abs(b) ) );\nv1 := [a, 0];\nv2 :
= [b, 0];\nwid := ceil( M/15) ;\n\nbar := arrow( v1, v2,\n    shape = \+
double_arrow, color = red , difference = true,\n    width = wid, head_
width = 0, head_length = 0):\n\ntextpos := max(wid, 2) ;\nLT := textpl
ot( [a, textpos, a] ):\nRT := textplot( [b, textpos, b] ):\n\nleftend \+
 := min( a - 2*wid, 0);\nrightend := max( b + 2*wid, 0);\n\nAxesplot :
= plot( 0, x = leftend..rightend , \n                     y = (-wid)..
(2*wid), axes = none, thickness = 2,\n                     scaling = c
onstrained, tickmarks = [1,1] ):\n\n\nif( leq ) then pt_color := red; \+
else pt_color := white; fi;\nleftpt := disk([ a, 0], wid/2, color=pt_c
olor):\nif( req ) then pt_color := red; else pt_color := white; fi;\nr
ightpt := disk([ b, 0], wid/2, color=pt_color ):\n\ndisplay(  leftpt, \+
rightpt, bar, Axesplot, LT, RT );\n\nend proc:\n" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 979 "intinfr := proc(a, leq  )\n#        descript
ion \"plot an infinite interval going to +inf\";\nlocal    bb, r, M, v
1, v2, wid, bar, Axesplot, textpos,\n         leftpt, rightpt, pt_colo
r, leftend, rightend, LT, RT;\n\nbb := 3*abs(a); \n\nr := bb-a;\nM := \+
evalf(1.2* max( abs(r), abs(a) ));\nv1 := [a, 0];\nv2 := [bb, 0];\nwid
 := ceil( M/15);\nbar := arrow( v1, v2,\n    shape = double_arrow, col
or = red , difference = true,\n   width = wid, head_width = 1.8*wid, h
ead_length = 1.2*wid):\n\ntextpos := max(wid, 3) ;\nLT := textplot( [a
, textpos, a] ):\nRT := textplot( [bb, textpos, `Infinity`] ): \n\nlef
tend := min( 0, a*1.5);\nrightend := max( 0, bb);\n\nAxesplot := plot(
 0, x = leftend..rightend , \n                     y = (-wid)..(3*wid)
, axes = none, thickness = 2,\n                     scaling = constrai
ned, tickmarks = [1,1] ):\n\n\nif( leq ) then pt_color := red; else pt
_color := white; fi;\nleftpt := disk([ a, 0], wid/2, color=pt_color):
\n\ndisplay(  leftpt,  bar, Axesplot, LT, RT );\n\nend proc:\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 986 "intinfl := proc( b, req  )
\n#        description \"plot a infinite interval going to -inf\";\nlo
cal    aa, bb, r, M, v1, v2, wid, bar, Axesplot,textpos, \n         le
ftpt, rightpt, pt_color, leftend, rightend, LT, RT;\n\naa := -3*abs(b)
; \n\nr := b-aa;\nM := evalf(1.2*max( abs(r), abs(b) ));\nv1 := [aa, 0
];\nv2 := [b, 0];\nwid := ceil( M/15);\nbar := arrow( v2, v1,\n    sha
pe = double_arrow, color = red , difference = true,\n   width = wid, h
ead_width = 1.8*wid, head_length = 1.2*wid):\n\ntextpos := max(wid, 3)
 ;\nLT := textplot( [aa, textpos, `-Infinity`] ):\nRT := textplot( [b,
 textpos, b] ): \n\nleftend := min( 0, aa);\nrightend := max( 0, b*1.5
);\n\nAxesplot := plot( 0, x = leftend..rightend , \n                 \+
    y = (-wid)..(3*wid), axes = none, thickness = 2,\n                \+
     scaling = constrained, tickmarks = [1,1] ):\n\n\nif( req ) then p
t_color := red; else pt_color := white; fi;\nrightpt := disk([ b, 0], \+
wid/2, color=pt_color):\n\ndisplay(  rightpt,  bar, Axesplot, LT, RT )
;\n\nend proc:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 840 "intall
 := proc()\n          #description \"plot a infinite interval of all r
eal numbers \";\nlocal    a, b, v1, v2, wid, bar1, bar2, LT, RT, Axesp
lot ;\na := -25; b := 25;\n\nv1 := [a, 0];\nv2 := [b, 0];\nwid := ceil
( (b-a)/15);\nbar1 := arrow( v1,\n    shape = double_arrow, color = re
d , difference = false,\n   width = wid, head_width = 1.8*wid, head_le
ngth = 1.2*wid):\n\nbar2 := arrow( v2,\n          shape = double_arrow
, color = red , difference = false,\n          width = wid, head_width
 = 1.8*wid, head_length = 1.2*wid):\n\nLT := textplot( [a, max( wid, 6
), `-Infinity`] ):\nRT := textplot( [b, max( wid, 6), `Infinity`] ): \+
\n\n\nAxesplot := plot( 0, x = a..b , \n                     y = (-wid
)..(3*wid), axes = none, thickness = 2,\n                     scaling \+
= constrained, tickmarks = [1,1] ):\n\ndisplay(  bar1, bar2, Axesplot,
 LT, RT );\nend proc:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 503 
"intv := proc( expr1, expr2  )\n        # description \"plot a infinit
e interval going to -inf\";\nlocal    a, b, leq, req;\n\nif type( expr
1, `<=`) then leq := true; else leq := false; fi;\nif type( expr2, `<=
`) then req := true; else req := false; fi;\na := lhs( expr1);     b :
= rhs( expr2);\n\nif( abs(a) <> infinity) \n  then if( abs(b) <> infin
ity) then intfin( a,b, leq, req );\n       else intinfr( a, leq);  fi;
\n  else if( abs(b) <> infinity) then intinfl( b, req);\n       else i
ntall(); fi;\n\nfi;\n\nend proc:" }}}{PARA 3 "" 0 "" {TEXT -1 0 "" }}}
{SECT 0 {PARA 3 "" 0 "" {TEXT -1 16 "Finite Intervals" }}{PARA 0 "" 0 
"" {TEXT -1 181 "Finite intervals may include one, both, or neither en
dpoint - depending on whether the inequalities are \"less than\", or \+
\"less than an equal\". This example is open on both endpoints." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
22 "intv( 3 < x, x < 17 );" }}}{PARA 0 "" 0 "" {TEXT -1 50 "While this
 example is closed on both endpoints ..." }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "intv( 10 <= x, x <= 200 );" }}}{PARA 0 "" 0 "" {TEXT 
-1 113 "\n\nIts also possible to have half-open  intervals (or half-cl
osed if you're a pessimist rather than an optimist). " }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 23 "intv( -30 <= x, x < 7);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 28 "intv( -140 < x,x <=  -110 );" }}}}{SECT 
0 {PARA 3 "" 0 "" {TEXT -1 18 "Infinite Intervals" }}{PARA 0 "" 0 "" 
{TEXT -1 123 "There are also infinite intervals. These occur when ther
e is only a single inequality, and no bound in the other direction." }
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "intv( -4 <  x, x < infinity
 );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "intv( -infinity < x,
 x < 10 );" }}}{PARA 0 "" 0 "" {TEXT -1 61 "\nIts also possible to hav
e infinite sets with closed endpoint" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 31 "intv( 10 <= x, x <  infinity );" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 32 "intv( -infinity < x, x <= 100 );" }}}{PARA 0 
"" 0 "" {TEXT -1 85 "\nAnd all real numbers can be represented as an i
nterval too....a really big interval." }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 36 "intv( -infinity < x, x < infinity );" }}}}{PARA 0 "" 
0 "" {TEXT 259 36 "\n         \251 2002 Waterloo Maple Inc " }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}}{MARK "0 1" 18 }{VIEWOPTS 1 1 0 1 1 1803 1 
1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }