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{SECT 0 {PARA 256 "" 0 "" {TEXT 256 50 "Precalculus Exploration 2: Pol
ynomial Inequalities" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT 274 192 "Use the following to explore and visualize how to gra
ph polynomial inequalities. Also, use the resultant graph to write dow
n the solution set of all x-coordinates that satisfy each inequality.
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 
20 "Sample Explorations " }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }
{TEXT 257 53 "Variation 1. Click in the red area and press [Enter]." }
}{PARA 0 "> " 0 "" {MPLTEXT 1 0 693 "f:=x->x^5-6*x^3+7*x:\n'f(x)'=f(x)
;\nfactor(f(x));\nop(sort([fsolve(f(x)=0,x)]));\n``*f(x) <= 0;\nwith(p
lottools):\np1:=plot(f(x),x=-3..-2.1,y=-4..4,color=blue,thickness=2):
\np2:=plot(f(x),x=-2.1..-1.26,color=red):\np3:=plot(f(x),x=-1.26..0,co
lor=blue,thickness=2):\np4:=plot(f(x),x=0..1.26,color=red):\np5:=plot(
f(x),x=1.26..2.1,color=blue,thickness=2):\np6:=plot(f(x),x=2.1..3,colo
r=red):\np7:=disk([-2.1,0],.1,color=blue):\np8:=disk([-1.26,0],.1,colo
r=blue):\np9:=disk([0,0],.1,color=blue):\np10:=disk([1.26,0],.1,color=
blue):\np11:=disk([2.1,0],.1,color=blue):\ngraph:=plots[display](\n   \+
     [p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11],\n         scaling=constrain
ed,\n         labels=[``,``]):\ngraph;\nwith(Logic):\n" }{TEXT -1 0 "
" }{MPLTEXT 1 0 102 "x<=-2.101002990,Export((-1.259280127<=x) &and (x<
=0)),\nExport((1.259280127<=x) &and (x<=2.101002990));" }{TEXT -1 0 "
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT 258 53 "Variation 2. Click in the red area and press [Enter
]." }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 799 "f:=x->x^5-6*x
^3+7*x:\n'f(x)'=f(x);\nfactor(f(x));\nop(sort([fsolve(f(x)=0,x)]));\n`
`*f(x) < 0;\nwith(plottools):\np1:=plot(f(x),x=-3..-2.1,y=-4..4,color=
blue,thickness=2):\np2:=plot(f(x),x=-2.1..-1.26,color=red):\np3:=plot(
f(x),x=-1.26..0,color=blue,thickness=2):\np4:=plot(f(x),x=0..1.26,colo
r=red):\np5:=plot(f(x),x=1.26..2.1,color=blue,thickness=2):\np6:=plot(
f(x),x=2.1..3,color=red):\np7:=circle([-2.1,0],.1,color=blue):\np8:=ci
rcle([-1.26,0],.1,color=blue):\np9:=circle([0,0],.1,color=blue):\np10:
=circle([1.26,0],.1,color=blue):\np11:=circle([2.1,0],.1,color=blue):
\ngraph:=plots[display](\n        [p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11]
,\n         scaling=constrained,\n         labels=[``,``]):\ngraph;\nw
ith(Logic):\nx<-2.101002990,Export((-1.259280127<x) &and (x<0)),\nExpo
rt((1.259280127<x) &and (x<2.101002990));" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 
259 110 "Variation 3. Click in the red area and press [Enter].\nWe add
 new variables here to make this easier to change." }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 961 "f:=x->x^5-6*x^3+7*x:\n'f(x)'=f(x);\nfactor(f(x));
\nop(sort([fsolve(f(x)=0,x)]));\n``*f(x) >= 0;\nwith(plottools):\ntopc
olor:=`blue`:\nbotcolor:=`red`:\ntopthick:=2:\nbotthick:=1:\np1:=plot(
f(x),x=-3..-2.1,y=-4..4,color=botcolor,thickness=botthick):\np2:=plot(
f(x),x=-2.1..-1.26,color=topcolor,thickness=topthick):\np3:=plot(f(x),
x=-1.26..0,color=botcolor,thickness=botthick):\np4:=plot(f(x),x=0..1.2
6,color=topcolor,thickness=topthick):\np5:=plot(f(x),x=1.26..2.1,color
=botcolor,thickness=botthick):\np6:=plot(f(x),x=2.1..3,color=topcolor,
thickness=topthick):\np7:=disk([-2.1,0],.1,color=blue):\np8:=disk([-1.
26,0],.1,color=blue):\np9:=disk([0,0],.1,color=blue):\np10:=disk([1.26
,0],.1,color=blue):\np11:=disk([2.1,0],.1,color=blue):\ngraph:=plots[d
isplay](\n        [p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11],\n         scal
ing=constrained,\n         labels=[``,``]):\ngraph;\nwith(Logic):\nExp
ort((-2.101002990<=x) &and (x<=-1.259280127)),\nExport((0<=x) &and (x<
=1.259280127)),2.101002990<=x;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 260 12 "Variation 4." }{TEXT 
-1 1 " " }{TEXT 269 40 "Click in the red area and press [Enter]." }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 965 "f:=x->x^5-6*x^3+7*x:\n'f(x)'=f(x);
\nfactor(f(x));\nop(sort([fsolve(f(x)=0,x)]));\n``*f(x) > 0;\nwith(plo
ttools):\ntopcolor:=`blue`:\nbotcolor:=`red`:\ntopthick:=2:\nbotthick:
=1:\np1:=plot(f(x),x=-3..-2.1,y=-4..4,color=botcolor,thickness=botthic
k):\np2:=plot(f(x),x=-2.1..-1.26,color=topcolor,thickness=topthick):\n
p3:=plot(f(x),x=-1.26..0,color=botcolor,thickness=botthick):\np4:=plot
(f(x),x=0..1.26,color=topcolor,thickness=topthick):\np5:=plot(f(x),x=1
.26..2.1,color=botcolor,thickness=botthick):\np6:=plot(f(x),x=2.1..3,c
olor=topcolor,thickness=topthick):\np7:=circle([-2.1,0],.1,color=blue)
:\np8:=circle([-1.26,0],.1,color=blue):\np9:=circle([0,0],.1,color=blu
e):\np10:=circle([1.26,0],.1,color=blue):\np11:=circle([2.1,0],.1,colo
r=blue):\ngraph:=plots[display](\n        [p1,p2,p3,p4,p5,p6,p7,p8,p9,
p10,p11],\n         scaling=constrained,\n         labels=[``,``]):\ng
raph;\nwith(Logic):\nExport((-2.101002990<x) &and (x<-1.259280127)),\n
Export((0<x) &and (x<1.259280127)),2.101002990<x;" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 22 "Ex
plorations Problem 1" }}{EXCHG {PARA 0 "" 0 "" {TEXT 266 96 "Change th
e Template below to correctly represent and graph the following functi
on and inequality" }{TEXT -1 2 ".\n" }{TEXT 270 40 "Click in the red a
rea and press [Enter]." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "(x^5-5*x^
3+4*x)>=0;\n`Change the defining expression for f below!!`;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }{TEXT 261 50 "Template. Click in the red area and press
 [Enter]." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "f:=x->x^5-6*x^3+7*x:" 
}{TEXT -1 0 "" }{TEXT 275 23 "Change function f here." }{TEXT -1 0 "" 
}{MPLTEXT 1 0 71 "\n'f(x)'=f(x);\nfactor(f(x));\nop(sort([fsolve(f(x)=
0,x)]));\n``*f(x) >= 0;" }{TEXT -1 0 "" }{TEXT 276 38 " Change inequal
ity here, if necessary." }{TEXT -1 0 "" }{MPLTEXT 1 0 767 "\nwith(plot
tools):\ntopcolor:=`blue`:\nbotcolor:=`red`:\ntopthick:=2:\nbotthick:=
1:\np1:=plot(f(x),x=-3..-2.1,y=-4..4,color=botcolor,thickness=botthick
):\np2:=plot(f(x),x=-2.1..-1.26,color=topcolor,thickness=topthick):\np
3:=plot(f(x),x=-1.26..0,color=botcolor,thickness=botthick):\np4:=plot(
f(x),x=0..1.26,color=topcolor,thickness=topthick):\np5:=plot(f(x),x=1.
26..2.1,color=botcolor,thickness=botthick):\np6:=plot(f(x),x=2.1..3,co
lor=topcolor,thickness=topthick):\np7:=disk([-2.1,0],.1,color=blue):\n
p8:=disk([-1.26,0],.1,color=blue):\np9:=disk([0,0],.1,color=blue):\np1
0:=disk([1.26,0],.1,color=blue):\np11:=disk([2.1,0],.1,color=blue):\ng
raph:=plots[display](\n        [p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11],\n
         scaling=constrained,\n         labels=[``,``]):\ngraph;\nwith
(Logic):" }{TEXT 277 41 " Change inequalities below, if necessary." }
{MPLTEXT 1 0 103 "\nx<=-2.101002990,Export((-1.259280127<=x) &and (x<=
0)),\nExport((1.259280127<=x) &and (x<=2.101002990));" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 
-1 22 "Explorations Problem 2" }}{EXCHG {PARA 0 "" 0 "" {TEXT 263 96 "
Change the Template below to correctly represent and graph the followi
ng function and inequality" }{TEXT -1 2 ".\n" }{TEXT 271 40 "Click in \+
the red area and press [Enter]." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 102 
"(x^4-4*x^2)<0;\n`Don't forget to change both the defining expression \+
for f and the inequality below!!`;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 262 
50 "Template. Click in the red area and press [Enter]." }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 20 "f:=x->x^5-6*x^3+7*x:" }{TEXT -1 0 "" }{TEXT 
278 24 " Change function f here." }{TEXT -1 1 " " }{MPLTEXT 1 0 72 "\n
'f(x)'=f(x);\nfactor(f(x));\nop(sort([fsolve(f(x)=0,x)]));\n``*f(x) >=
 0; " }{TEXT 280 37 "Change inequality here, if necessary." }{MPLTEXT 
1 0 767 "\nwith(plottools):\ntopcolor:=`blue`:\nbotcolor:=`red`:\ntopt
hick:=2:\nbotthick:=1:\np1:=plot(f(x),x=-3..-2.1,y=-4..4,color=botcolo
r,thickness=botthick):\np2:=plot(f(x),x=-2.1..-1.26,color=topcolor,thi
ckness=topthick):\np3:=plot(f(x),x=-1.26..0,color=botcolor,thickness=b
otthick):\np4:=plot(f(x),x=0..1.26,color=topcolor,thickness=topthick):
\np5:=plot(f(x),x=1.26..2.1,color=botcolor,thickness=botthick):\np6:=p
lot(f(x),x=2.1..3,color=topcolor,thickness=topthick):\np7:=disk([-2.1,
0],.1,color=blue):\np8:=disk([-1.26,0],.1,color=blue):\np9:=disk([0,0]
,.1,color=blue):\np10:=disk([1.26,0],.1,color=blue):\np11:=disk([2.1,0
],.1,color=blue):\ngraph:=plots[display](\n        [p1,p2,p3,p4,p5,p6,
p7,p8,p9,p10,p11],\n         scaling=constrained,\n         labels=[``
,``]):\ngraph;\nwith(Logic):" }{TEXT -1 1 " " }{TEXT 279 40 "Change in
equalities below, if necessary." }{MPLTEXT 1 0 104 " \nx<=-2.101002990
,Export((-1.259280127<=x) &and (x<=0)),\nExport((1.259280127<=x) &and \+
(x<=2.101002990));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
{SECT 1 {PARA 3 "" 0 "" {TEXT -1 22 "Explorations Problem 3" }}{EXCHG 
{PARA 0 "" 0 "" {TEXT 267 96 "Change the Template below to correctly r
epresent and graph the following function and inequality" }{TEXT -1 2 
".\n" }{TEXT 272 40 "Click in the red area and press [Enter]." }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "(3*x^3-7*x^2-6*x)<=0;\n`Don't forg
et to change both the defining expression for f and the inequality bel
ow!!`;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 0 "" }{TEXT 264 50 "Template. Click in the red area
 and press [Enter]." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "f:=x->x^5-6*
x^3+7*x: " }{TEXT -1 0 "" }{TEXT 281 23 "Change function f here." }
{TEXT -1 0 "" }{MPLTEXT 1 0 72 "\n'f(x)'=f(x);\nfactor(f(x));\nop(sort
([fsolve(f(x)=0,x)]));\n``*f(x) >= 0; " }{TEXT 283 37 "Change inequali
ty here, if necessary." }{TEXT -1 0 "" }{MPLTEXT 1 0 768 "\nwith(plott
ools):\ntopcolor:=`blue`:\nbotcolor:=`red`:\ntopthick:=2:\nbotthick:=1
:\np1:=plot(f(x),x=-3..-2.1,y=-4..4,color=botcolor,thickness=botthick)
:\np2:=plot(f(x),x=-2.1..-1.26,color=topcolor,thickness=topthick):\np3
:=plot(f(x),x=-1.26..0,color=botcolor,thickness=botthick):\np4:=plot(f
(x),x=0..1.26,color=topcolor,thickness=topthick):\np5:=plot(f(x),x=1.2
6..2.1,color=botcolor,thickness=botthick):\np6:=plot(f(x),x=2.1..3,col
or=topcolor,thickness=topthick):\np7:=disk([-2.1,0],.1,color=blue):\np
8:=disk([-1.26,0],.1,color=blue):\np9:=disk([0,0],.1,color=blue):\np10
:=disk([1.26,0],.1,color=blue):\np11:=disk([2.1,0],.1,color=blue):\ngr
aph:=plots[display](\n        [p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11],\n \+
        scaling=constrained,\n         labels=[``,``]):\ngraph;\nwith(
Logic): " }{TEXT 285 40 "Change inequalities below, if necessary." }
{TEXT -1 0 "" }{MPLTEXT 1 0 104 " \nx<=-2.101002990,Export((-1.2592801
27<=x) &and (x<=0)),\nExport((1.259280127<=x) &and (x<=2.101002990));
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "
" 0 "" {TEXT -1 22 "Explorations Problem 4" }}{EXCHG {PARA 0 "" 0 "" 
{TEXT 268 96 "Change the Template below to correctly represent and gra
ph the following function and inequality" }{TEXT -1 2 ".\n" }{TEXT 
273 40 "Click in the red area and press [Enter]." }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 108 "(x^4+4*x^3+4*x^2)>0;\n`Don't forget to change both t
he defining expression for f and the inequality below!!`;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 0 "" }{TEXT 265 50 "Template. Click in the red area and press [Ente
r]." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "f:=x->x^5-6*x^3+7*x: " }
{TEXT -1 0 "" }{TEXT 282 23 "Change function f here." }{TEXT -1 0 "" }
{MPLTEXT 1 0 73 " \n'f(x)'=f(x);\nfactor(f(x));\nop(sort([fsolve(f(x)=
0,x)]));\n``*f(x) >= 0; " }{TEXT 284 37 "Change inequality here, if ne
cessary." }{TEXT -1 0 "" }{MPLTEXT 1 0 768 "\nwith(plottools):\ntopcol
or:=`blue`:\nbotcolor:=`red`:\ntopthick:=2:\nbotthick:=1:\np1:=plot(f(
x),x=-3..-2.1,y=-4..4,color=botcolor,thickness=botthick):\np2:=plot(f(
x),x=-2.1..-1.26,color=topcolor,thickness=topthick):\np3:=plot(f(x),x=
-1.26..0,color=botcolor,thickness=botthick):\np4:=plot(f(x),x=0..1.26,
color=topcolor,thickness=topthick):\np5:=plot(f(x),x=1.26..2.1,color=b
otcolor,thickness=botthick):\np6:=plot(f(x),x=2.1..3,color=topcolor,th
ickness=topthick):\np7:=disk([-2.1,0],.1,color=blue):\np8:=disk([-1.26
,0],.1,color=blue):\np9:=disk([0,0],.1,color=blue):\np10:=disk([1.26,0
],.1,color=blue):\np11:=disk([2.1,0],.1,color=blue):\ngraph:=plots[dis
play](\n        [p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11],\n         scalin
g=constrained,\n         labels=[``,``]):\ngraph;\nwith(Logic): " }
{TEXT 286 40 "Change inequalities below, if necessary." }{TEXT -1 0 "
" }{MPLTEXT 1 0 104 " \nx<=-2.101002990,Export((-1.259280127<=x) &and \+
(x<=0)),\nExport((1.259280127<=x) &and (x<=2.101002990));" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT -1 37 "_____________________________________" 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 30 "Filenam
e: ExplorePrecalc02.mws" }}{PARA 0 "" 0 "" {TEXT -1 36 "Copyright 2005
, All Rights Reserved." }}{PARA 0 "" 0 "" {TEXT -1 44 "Permission is g
ranted to use and modify for " }}{PARA 0 "" 0 "" {TEXT -1 37 "academic
 and non-commercial purposes." }}{PARA 0 "" 0 "" {TEXT -1 13 "Dr. John
 Pais" }}{PARA 0 "" 0 "" {TEXT -1 28 "Mathematics Department-MICDS" }}
{PARA 0 "" 0 "" {TEXT -1 45 "E-mail: pais@micds.org or pais@kinetigram
.com" }}{PARA 0 "" 0 "" {TEXT -1 33 "URL:  http://kinetigram.com/micds
" }}{PARA 0 "" 0 "" {TEXT -1 37 "_____________________________________
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{MARK "0 0" 23 }{VIEWOPTS 1 1 0 
1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }