Interactive Algebra & Trigonometry - A Self Guided Study Companion

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Confidence	Program	Detection	Match Type	Support
`1%`	dexvert	Eclipse Tutorial `(other/eclipseTutorial)`	ext	Unsupported
`1%`	dexvert	JuggleKrazy Tutorial `(other/juggleKrazyTutorial)`	ext	Unsupported
`100%`	file	data	default
`100%`	gt2	Kopftext: 'TUTOR 06'	default (weak)
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|00000d80| 00 74 6f 20 74 68 65 20 | 11 33 79 11 31 2d 61 78 |.to the |.3y.1-ax|
|00000d90| 69 73 2c 20 77 65 20 63 | 6f 6e 63 6c 75 64 65 20 |is, we c|onclude |
|00000da0| 74 68 61 74 20 69 74 20 | 69 73 20 6e 65 69 74 68 |that it |is neith|
|00000db0| 65 72 20 65 76 65 6e 20 | 6e 6f 72 20 6f 64 64 2e |er even |nor odd.|
|00000dc0| 0d 0a 00 53 65 63 74 69 | 6f 6e 20 32 2e 33 20 20 |...Secti|on 2.3  |
|00000dd0| 41 6e 61 6c 79 7a 69 6e | 67 20 47 72 61 70 68 73 |Analyzin|g Graphs|
|00000de0| 20 6f 66 20 46 75 6e 63 | 74 69 6f 6e 73 0d 0b 00 | of Func|tions...|
|00000df0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00000e00| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00000e10| 20 20 20 20 20 20 20 20 | 11 32 33 0d 0b 00 11 31 |        |.23....1|
|00000e20| 44 65 74 65 72 6d 69 6e | 65 20 77 68 65 74 68 65 |Determin|e whethe|
|00000e30| 72 20 74 68 65 20 66 75 | 6e 63 74 69 6f 6e 20 11 |r the fu|nction .|
|00000e40| 33 66 11 31 28 11 33 78 | 11 31 29 20 3d 20 33 11 |3f.1(.3x|.1) = 3.|
|00000e50| 33 78 20 20 11 31 2d 20 | 35 11 33 78 20 11 31 69 |3x  .1- |5.3x .1i|
|00000e60| 73 20 65 76 65 6e 2c 20 | 6f 64 64 2c 20 6f 72 20 |s even, |odd, or |
|00000e70| 6e 65 69 74 68 65 72 2e | 0d 0a 00 0d 0a 00 13 12 |neither.|........|
|00000e80| 31 53 4f 4c 55 54 49 4f | 4e 12 30 0d 0a 00 0d 0b |1SOLUTIO|N.0.....|
|00000e90| 00 54 6f 20 64 65 74 65 | 72 6d 69 6e 65 20 77 68 |.To dete|rmine wh|
|00000ea0| 65 74 68 65 72 20 74 68 | 65 20 66 75 6e 63 74 69 |ether th|e functi|
|00000eb0| 6f 6e 20 69 73 20 65 76 | 65 6e 20 6f 72 20 6f 64 |on is ev|en or od|
|00000ec0| 64 2c 20 77 65 20 72 65 | 70 6c 61 63 65 20 11 33 |d, we re|place .3|
|00000ed0| 78 20 11 31 62 79 20 2d | 11 33 78 20 11 31 61 6e |x .1by -|.3x .1an|
|00000ee0| 64 0d 0a 00 6f 62 74 61 | 69 6e 0d 0a 00 20 20 20 |d...obta|in...   |
|00000ef0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00000f00| 20 20 20 20 20 20 20 11 | 32 33 0d 0b 00 20 20 20 |       .|23...   |
|00000f10| 20 20 20 20 20 20 20 20 | 20 20 11 33 66 11 31 28 |        |  .3f.1(|
|00000f20| 2d 11 33 78 11 31 29 20 | 3d 20 33 28 2d 11 33 78 |-.3x.1) |= 3(-.3x|
|00000f30| 11 31 29 20 20 2d 20 35 | 28 2d 11 33 78 11 31 29 |.1)  - 5|(-.3x.1)|
|00000f40| 13 0d 0a 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |....    |        |
|00000f50| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 32 33 0d |        |    .23.|
|00000f60| 0b 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |..      |        |
|00000f70| 20 20 20 20 20 11 31 3d | 20 2d 33 11 33 78 20 20 |     .1=| -3.3x  |
|00000f80| 11 31 2b 20 35 11 33 78 | 11 31 13 0d 0a 00 20 20 |.1+ 5.3x|.1....  |
|00000f90| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00000fa0| 20 20 20 20 20 20 20 11 | 32 33 0d 0b 00 20 20 20 |       .|23...   |
|00000fb0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00000fc0| 11 31 3d 20 2d 28 33 11 | 33 78 20 20 11 31 2d 20 |.1= -(3.|3x  .1- |
|00000fd0| 35 11 33 78 11 31 29 13 | 0d 0a 00 0d 0b 00 20 20 |5.3x.1).|......  |
|00000fe0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00000ff0| 20 3d 20 2d 11 33 66 11 | 31 28 11 33 78 11 31 29 | = -.3f.|1(.3x.1)|
|00001000| 13 0d 0a 00 0d 0b 00 42 | 65 63 61 75 73 65 20 74 |.......B|ecause t|
|00001010| 68 69 73 20 72 65 70 6c | 61 63 65 6d 65 6e 74 20 |his repl|acement |
|00001020| 70 72 6f 64 75 63 65 64 | 20 2d 11 33 66 11 31 28 |produced| -.3f.1(|
|00001030| 11 33 78 11 31 29 2c 20 | 77 65 20 63 6f 6e 63 6c |.3x.1), |we concl|
|00001040| 75 64 65 20 74 68 61 74 | 20 74 68 65 20 66 75 6e |ude that| the fun|
|00001050| 63 74 69 6f 6e 20 69 73 | 20 6f 64 64 2e 0d 0a 00 |ction is| odd....|
|00001060| 53 65 63 74 69 6f 6e 20 | 32 2e 33 20 20 41 6e 61 |Section |2.3  Ana|
|00001070| 6c 79 7a 69 6e 67 20 47 | 72 61 70 68 73 20 6f 66 |lyzing G|raphs of|
|00001080| 20 46 75 6e 63 74 69 6f | 6e 73 0d 0b 00 53 6b 65 | Functio|ns...Ske|
|00001090| 74 63 68 20 74 68 65 20 | 67 72 61 70 68 20 6f 66 |tch the |graph of|
|000010a0| 20 74 68 65 20 66 75 6e | 63 74 69 6f 6e 20 11 33 | the fun|ction .3|
|000010b0| 66 11 31 28 11 33 78 11 | 31 29 20 3d 20 2d 32 20 |f.1(.3x.|1) = -2 |
|000010c0| 61 6e 64 20 64 65 74 65 | 72 6d 69 6e 65 20 77 68 |and dete|rmine wh|
|000010d0| 65 74 68 65 72 20 74 68 | 65 20 66 75 6e 63 74 69 |ether th|e functi|
|000010e0| 6f 6e 0d 0a 00 69 73 20 | 65 76 65 6e 2c 20 6f 64 |on...is |even, od|
|000010f0| 64 2c 20 6f 72 20 6e 65 | 69 74 68 65 72 2e 0d 0a |d, or ne|ither...|
|00001100| 00 0d 0b 00 13 12 31 53 | 4f 4c 55 54 49 4f 4e 12 |......1S|OLUTION.|
|00001110| 30 0d 0a 00 0d 0b 00 53 | 69 6e 63 65 20 11 33 66 |0......S|ince .3f|
|00001120| 20 11 31 69 73 20 61 20 | 63 6f 6e 73 74 61 6e 74 | .1is a |constant|
|00001130| 20 66 75 6e 63 74 69 6f | 6e 2c 20 77 65 20 6b 6e | functio|n, we kn|
|00001140| 6f 77 0d 0a 00 74 68 61 | 74 20 69 74 73 20 67 72 |ow...tha|t its gr|
|00001150| 61 70 68 20 69 73 20 61 | 20 68 6f 72 69 7a 6f 6e |aph is a| horizon|
|00001160| 74 61 6c 20 6c 69 6e 65 | 20 61 73 0d 0a 00 73 68 |tal line| as...sh|
|00001170| 6f 77 6e 20 69 6e 20 74 | 68 65 20 66 69 67 75 72 |own in t|he figur|
|00001180| 65 20 61 74 20 74 68 65 | 20 72 69 67 68 74 2e 20 |e at the| right. |
|00001190| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 14 6b 33 |        |     .k3|
|000011a0| 2d 35 2d 35 2e 6d 14 34 | 39 14 31 30 14 34 30 14 |-5-5.m.4|9.10.40.|
|000011b0| 38 14 20 20 20 20 20 20 | 20 13 0d 0a 00 0d 0b 00 |8.      | .......|
|000011c0| 53 69 6e 63 65 20 74 68 | 69 73 20 67 72 61 70 68 |Since th|is graph|
|000011d0| 20 69 73 20 73 79 6d 6d | 65 74 72 69 63 20 77 69 | is symm|etric wi|
|000011e0| 74 68 20 72 65 73 70 65 | 63 74 0d 0a 00 74 6f 20 |th respe|ct...to |
|000011f0| 74 68 65 20 11 33 79 11 | 31 2d 61 78 69 73 2c 20 |the .3y.|1-axis, |
|00001200| 77 65 20 63 6f 6e 63 6c | 75 64 65 20 74 68 61 74 |we concl|ude that|
|00001210| 20 74 68 65 20 66 75 6e | 63 74 69 6f 6e 0d 0a 00 | the fun|ction...|
|00001220| 69 73 20 65 76 65 6e 2e | 13 0d 0a 00 0d 0b 00 54 |is even.|.......T|
|00001230| 6f 20 76 65 72 69 66 79 | 20 74 68 69 73 20 72 65 |o verify| this re|
|00001240| 73 75 6c 74 2c 20 73 68 | 6f 77 20 74 68 61 74 20 |sult, sh|ow that |
|00001250| 11 33 66 11 31 28 2d 11 | 33 78 11 31 29 20 3d 20 |.3f.1(-.|3x.1) = |
|00001260| 11 33 66 11 31 28 11 33 | 78 11 31 29 2e 0d 0a 00 |.3f.1(.3|x.1)....|
|00001270| 53 65 63 74 69 6f 6e 20 | 32 2e 33 20 20 41 6e 61 |Section |2.3  Ana|
|00001280| 6c 79 7a 69 6e 67 20 47 | 72 61 70 68 73 20 6f 66 |lyzing G|raphs of|
|00001290| 20 46 75 6e 63 74 69 6f | 6e 73 0d 0b 00 20 20 20 | Functio|ns...   |
|000012a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000012b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000012c0| 20 20 20 20 20 20 20 11 | 32 33 0d 0b 00 11 31 53 |       .|23....1S|
|000012d0| 6b 65 74 63 68 20 74 68 | 65 20 67 72 61 70 68 20 |ketch th|e graph |
|000012e0| 6f 66 20 74 68 65 20 66 | 75 6e 63 74 69 6f 6e 20 |of the f|unction |
|000012f0| 11 33 66 11 31 28 11 33 | 78 11 31 29 20 3d 20 32 |.3f.1(.3|x.1) = 2|
|00001300| 11 33 78 20 20 11 31 61 | 6e 64 20 64 65 74 65 72 |.3x  .1a|nd deter|
|00001310| 6d 69 6e 65 20 77 68 65 | 74 68 65 72 20 74 68 65 |mine whe|ther the|
|00001320| 20 66 75 6e 63 74 69 6f | 6e 0d 0a 00 69 73 20 65 | functio|n...is e|
|00001330| 76 65 6e 2c 20 6f 64 64 | 2c 20 6f 72 20 6e 65 69 |ven, odd|, or nei|
|00001340| 74 68 65 72 2e 0d 0a 00 | 0d 0b 00 13 12 31 53 4f |ther....|.....1SO|
|00001350| 4c 55 54 49 4f 4e 12 30 | 0d 0a 00 55 73 69 6e 67 |LUTION.0|...Using|
|00001360| 20 74 68 65 20 70 6f 69 | 6e 74 2d 70 6c 6f 74 74 | the poi|nt-plott|
|00001370| 69 6e 67 20 6d 65 74 68 | 6f 64 20 61 73 20 64 65 |ing meth|od as de|
|00001380| 73 63 72 69 62 65 64 0d | 0a 00 69 6e 20 53 65 63 |scribed.|..in Sec|
|00001390| 74 69 6f 6e 20 31 2e 31 | 20 6f 66 20 74 68 65 20 |tion 1.1| of the |
|000013a0| 74 65 78 74 2c 20 61 6e | 64 20 6f 75 72 20 6b 6e |text, an|d our kn|
|000013b0| 6f 77 6c 65 64 67 65 0d | 0a 00 6f 66 20 74 68 65 |owledge.|..of the|
|000013c0| 20 67 65 6e 65 72 61 6c | 20 73 68 61 70 65 20 6f | general| shape o|
|000013d0| 66 20 74 68 65 20 67 72 | 61 70 68 20 6f 66 20 61 |f the gr|aph of a|
|000013e0| 20 63 75 62 69 63 0d 0a | 00 66 75 6e 63 74 69 6f | cubic..|.functio|
|000013f0| 6e 2c 20 77 65 20 6f 62 | 74 61 69 6e 20 74 68 65 |n, we ob|tain the|
|00001400| 20 67 72 61 70 68 20 73 | 68 6f 77 6e 20 61 74 20 | graph s|hown at |
|00001410| 74 68 65 0d 0a 00 72 69 | 67 68 74 2e 20 20 20 20 |the...ri|ght.    |
|00001420| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001430| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001440| 20 20 20 20 20 20 14 6b | 33 2d 35 2d 36 2e 6d 14 |      .k|3-5-6.m.|
|00001450| 34 38 14 38 14 34 30 14 | 38 14 20 20 13 0d 0a 00 |48.8.40.|8.  ....|
|00001460| 0d 0b 00 57 65 20 63 61 | 6e 20 73 65 65 20 66 72 |...We ca|n see fr|
|00001470| 6f 6d 20 6f 75 72 20 73 | 6b 65 74 63 68 20 74 68 |om our s|ketch th|
|00001480| 61 74 20 74 68 65 20 67 | 72 61 70 68 20 6f 66 0d |at the g|raph of.|
|00001490| 0a 00 74 68 69 73 20 66 | 75 6e 63 74 69 6f 6e 20 |..this f|unction |
|000014a0| 69 73 20 73 79 6d 6d 65 | 74 72 69 63 20 77 69 74 |is symme|tric wit|
|000014b0| 68 20 72 65 73 70 65 63 | 74 20 74 6f 0d 0a 00 74 |h respec|t to...t|
|000014c0| 68 65 20 6f 72 69 67 69 | 6e 2e 13 0d 0a 00 0d 0b |he origi|n.......|
|000014d0| 00 54 68 65 72 65 66 6f | 72 65 2c 20 77 65 20 63 |.Therefo|re, we c|
|000014e0| 6f 6e 63 6c 75 64 65 20 | 74 68 61 74 20 74 68 65 |onclude |that the|
|000014f0| 20 66 75 6e 63 74 69 6f | 6e 20 69 73 20 6f 64 64 | functio|n is odd|
|00001500| 2e 20 20 59 6f 75 20 63 | 61 6e 20 63 68 65 63 6b |.  You c|an check|
|00001510| 20 74 68 69 73 20 72 65 | 73 75 6c 74 20 62 79 0d | this re|sult by.|
|00001520| 0a 00 73 68 6f 77 69 6e | 67 20 74 68 61 74 20 11 |..showin|g that .|
|00001530| 33 66 11 31 28 2d 11 33 | 78 11 31 29 20 3d 20 2d |3f.1(-.3|x.1) = -|
|00001540| 11 33 66 11 31 28 11 33 | 78 11 31 29 2e 0d 0a 00 |.3f.1(.3|x.1)....|
|00001550| 53 65 63 74 69 6f 6e 20 | 32 2e 33 20 20 41 6e 61 |Section |2.3  Ana|
|00001560| 6c 79 7a 69 6e 67 20 47 | 72 61 70 68 73 20 6f 66 |lyzing G|raphs of|
|00001570| 20 46 75 6e 63 74 69 6f | 6e 73 0d 0b 00 53 6b 65 | Functio|ns...Ske|
|00001580| 74 63 68 20 74 68 65 20 | 67 72 61 70 68 20 6f 66 |tch the |graph of|
|00001590| 20 74 68 65 20 66 75 6e | 63 74 69 6f 6e 20 61 6e | the fun|ction an|
|000015a0| 64 20 64 65 74 65 72 6d | 69 6e 65 20 77 68 65 74 |d determ|ine whet|
|000015b0| 68 65 72 20 74 68 65 20 | 66 75 6e 63 74 69 6f 6e |her the |function|
|000015c0| 20 69 73 20 65 76 65 6e | 2c 0d 0a 00 6f 64 64 2c | is even|,...odd,|
|000015d0| 20 6f 72 20 6e 65 69 74 | 68 65 72 2e 0d 0b 00 20 | or neit|her.... |
|000015e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000015f0| 20 20 20 20 20 20 20 20 | 20 20 11 34 28 0d 0b 00 |        |  .4(...|
|00001600| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001610| 20 20 20 20 20 20 20 20 | 20 20 20 21 20 11 31 32 |        |   ! .12|
|00001620| 20 2d 20 11 33 78 11 31 | 2c 20 20 20 11 33 78 20 | - .3x.1|,   .3x |
|00001630| 11 34 3c 20 11 31 30 0d | 0b 00 20 20 20 20 20 20 |.4< .10.|..      |
|00001640| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001650| 20 20 20 20 20 11 34 21 | 0d 0b 00 20 20 20 20 20 |     .4!|...     |
|00001660| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 |        |       .|
|00001670| 33 66 11 31 28 11 33 78 | 11 31 29 20 3d 20 11 34 |3f.1(.3x|.1) = .4|
|00001680| 7b 20 11 31 32 2c 20 20 | 20 20 20 20 20 30 20 3c |{ .12,  |     0 <|
|00001690| 20 11 33 78 20 11 34 3c | 20 11 31 33 0d 0b 00 20 | .3x .4<| .13... |
|000016a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000016b0| 20 20 20 20 20 20 20 20 | 20 20 11 34 21 0d 0b 00 |        |  .4!...|
|000016c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000016d0| 20 20 20 20 20 20 20 20 | 20 20 20 21 20 11 31 38 |        |   ! .18|
|000016e0| 20 2d 20 32 11 33 78 11 | 31 2c 20 20 11 33 78 20 | - 2.3x.|1,  .3x |
|000016f0| 11 31 3e 20 33 0d 0b 00 | 20 20 20 20 20 20 20 20 |.1> 3...|        |
|00001700| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001710| 20 20 20 11 34 39 0d 0a | 00 11 31 13 12 31 53 4f |   .49..|..1..1SO|
|00001720| 4c 55 54 49 4f 4e 12 30 | 0d 0a 00 0d 0b 00 57 68 |LUTION.0|......Wh|
|00001730| 65 6e 20 11 33 78 20 11 | 34 3c 20 11 31 30 2c 20 |en .3x .|4< .10, |
|00001740| 74 68 65 20 66 75 6e 63 | 74 69 6f 6e 20 69 73 20 |the func|tion is |
|00001750| 64 65 66 69 6e 65 64 20 | 62 79 20 74 68 65 0d 0a |defined |by the..|
|00001760| 00 65 71 75 61 74 69 6f | 6e 20 32 20 2d 20 11 33 |.equatio|n 2 - .3|
|00001770| 78 11 31 2e 20 20 54 68 | 75 73 2c 20 77 65 20 6f |x.1.  Th|us, we o|
|00001780| 62 74 61 69 6e 20 74 68 | 65 20 70 6f 72 74 69 6f |btain th|e portio|
|00001790| 6e 0d 0a 00 6f 66 20 74 | 68 65 20 67 72 61 70 68 |n...of t|he graph|
|000017a0| 20 73 68 6f 77 6e 20 61 | 74 20 74 68 65 20 72 69 | shown a|t the ri|
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|000017c0| 14 6b 33 2d 35 2d 37 61 | 2e 6d 14 34 38 14 31 36 |.k3-5-7a|.m.48.16|
|000017d0| 14 34 30 14 38 14 20 20 | 20 20 13 0d 0a 00 57 68 |.40.8.  |  ....Wh|
|000017e0| 65 6e 20 30 20 3c 20 11 | 33 78 20 11 34 3c 20 11 |en 0 < .|3x .4< .|
|000017f0| 31 33 2c 20 74 68 65 20 | 66 75 6e 63 74 69 6f 6e |13, the |function|
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|00001810| 0a 00 76 61 6c 75 65 20 | 6f 66 20 32 2e 20 20 20 |..value |of 2.   |
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|00001830| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 14 6b |        |      .k|
|00001840| 33 2d 35 2d 37 62 2e 6d | 14 34 38 14 31 36 14 34 |3-5-7b.m|.48.16.4|
|00001850| 30 14 38 14 20 20 20 20 | 13 0d 0a 00 57 68 65 6e |0.8.    |....When|
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|00001890| 61 74 69 6f 6e 20 38 20 | 2d 20 32 11 33 78 20 11 |ation 8 |- 2.3x .|
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|000018b0| 20 74 68 65 20 67 72 61 | 70 68 20 61 73 0d 0a 00 | the gra|ph as...|
|000018c0| 73 68 6f 77 6e 2e 20 20 | 20 20 20 20 20 20 20 20 |shown.  |        |
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|00001900| 38 14 20 20 20 20 13 0d | 0a 00 0d 0a 00 53 69 6e |8.    ..|.....Sin|
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|00001930| 69 74 68 20 72 65 73 70 | 65 63 74 20 74 6f 20 74 |ith resp|ect to t|
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|00001950| 74 68 20 72 65 73 70 65 | 63 74 0d 0a 00 74 6f 20 |th respe|ct...to |
|00001960| 74 68 65 20 11 33 79 11 | 31 2d 61 78 69 73 2c 20 |the .3y.|1-axis, |
|00001970| 77 65 20 63 6f 6e 63 6c | 75 64 65 20 74 68 61 74 |we concl|ude that|
|00001980| 20 69 74 20 69 73 20 6e | 65 69 74 68 65 72 20 65 | it is n|either e|
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|00001a10| 20 3d 20 11 33 78 20 20 | 11 31 2d 20 31 2c 20 61 | = .3x  |.1- 1, a|
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|00001a30| 20 69 6e 74 65 72 76 61 | 6c 28 73 29 20 28 69 66 | interva|l(s) (if|
|00001a40| 20 61 6e 79 29 20 6f 6e | 0d 0a 00 74 68 65 20 72 | any) on|...the r|
|00001a50| 65 61 6c 20 61 78 69 73 | 20 74 68 61 74 20 11 33 |eal axis| that .3|
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|00001aa0| 20 64 65 73 63 72 69 62 | 65 64 20 69 6e 20 53 65 | describ|ed in Se|
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|00001ac0| 68 65 20 74 65 78 74 2c | 20 61 6e 64 20 6f 75 72 |he text,| and our|
|00001ad0| 20 6b 6e 6f 77 6c 65 64 | 67 65 20 6f 66 20 74 68 | knowled|ge of th|
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|00001af0| 65 20 6f 66 20 74 68 65 | 20 67 72 61 70 68 20 6f |e of the| graph o|
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|00001b20| 69 6e 20 74 68 65 20 67 | 72 61 70 68 20 73 68 6f |in the g|raph sho|
|00001b30| 77 6e 20 61 74 20 74 68 | 65 0d 0a 00 72 69 67 68 |wn at th|e...righ|
|00001b40| 74 2e 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |t.      |        |
|00001b50| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001b60| 20 20 20 20 20 20 20 20 | 20 14 6b 33 2d 35 2d 39 |        | .k3-5-9|
|00001b70| 2e 6d 14 34 38 14 31 32 | 14 34 30 14 38 14 20 20 |.m.48.12|.40.8.  |
|00001b80| 20 13 0d 0a 00 0d 0b 00 | 54 6f 20 64 65 74 65 72 | .......|To deter|
|00001b90| 6d 69 6e 65 20 77 68 65 | 72 65 20 74 68 65 20 66 |mine whe|re the f|
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|00001bb0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001bc0| 20 20 11 32 32 0d 0b 00 | 11 31 6e 6f 6e 6e 65 67 |  .22...|.1nonneg|
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|00001be0| 20 20 11 31 2d 20 31 20 | 11 34 3e 20 11 31 30 2e |  .1- 1 |.4> .10.|
|00001bf0| 20 13 0d 0a 00 0d 0a 00 | 0d 0b 00 44 6f 69 6e 67 | .......|...Doing|
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|00001c10| 20 74 68 65 20 74 65 73 | 74 20 69 6e 74 65 72 76 | the tes|t interv|
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|00001c30| 2c 20 28 2d 31 2c 20 31 | 29 2c 20 61 6e 64 20 28 |, (-1, 1|), and (|
|00001c40| 31 2c 20 11 34 38 11 31 | 29 2e 20 20 13 0d 0a 00 |1, .48.1|).  ....|
|00001c50| 0d 0b 00 54 65 73 74 69 | 6e 67 20 74 68 65 73 65 |...Testi|ng these|
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|00001c80| 33 78 11 31 29 20 11 34 | 3e 20 11 31 30 20 6f 6e |3x.1) .4|> .10 on|
|00001c90| 20 74 68 65 20 69 6e 74 | 65 72 76 61 6c 73 20 28 | the int|ervals (|
|00001ca0| 2d 11 34 38 11 31 2c 20 | 2d 31 5d 20 61 6e 64 20 |-.48.1, |-1] and |
|00001cb0| 0d 0a 00 5b 31 2c 20 11 | 34 38 11 31 29 2e 0d 0a |...[1, .|48.1)...|
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|00001cd0| 00 00 00 00 00 65 32 2d | 33 00 ee 02 00 00 47 02 |.....e2-|3.....G.|
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|00001d00| 00 35 05 00 00 00 00 00 | 00 65 32 2d 33 2d 32 00 |.5......|.e2-3-2.|
|00001d10| 5f 07 00 00 7b 01 00 00 | 4d 2a 00 00 35 07 00 00 |_...{...|M*..5...|
|00001d20| 00 00 00 00 65 32 2d 33 | 2d 33 00 04 09 00 00 bf |....e2-3|-3......|
|00001d30| 04 00 00 4d 2a 00 00 da | 08 00 00 00 00 00 00 65 |...M*...|.......e|
|00001d40| 32 2d 33 2d 34 00 ed 0d | 00 00 73 02 00 00 4d 2a |2-3-4...|..s...M*|
|00001d50| 00 00 c3 0d 00 00 00 00 | 00 00 65 32 2d 33 2d 35 |........|..e2-3-5|
|00001d60| 00 8a 10 00 00 e6 01 00 | 00 4d 2a 00 00 60 10 00 |........|.M*..`..|
|00001d70| 00 00 00 00 00 69 32 2d | 33 2d 31 00 9a 12 00 00 |.....i2-|3-1.....|
|00001d80| b6 02 00 00 4d 2a 00 00 | 70 12 00 00 00 00 00 00 |....M*..|p.......|
|00001d90| 69 32 2d 33 2d 32 00 7a | 15 00 00 25 04 00 00 4d |i2-3-2.z|...%...M|
|00001da0| 2a 00 00 50 15 00 00 00 | 00 00 00 69 32 2d 33 2d |*..P....|...i2-3-|
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|00001dc0| 00 00 00 00 00 00 69 32 | 2d 33 2d 34 00          |......i2|-3-4.   |
+--------+-------------------------+-------------------------+--------+--------+