home *** CD-ROM | disk | FTP | other *** search
| Unknown | 1996-08-15 | 11.5 KB |
open in: 
MacOS 8.1
|
Win98
|
DOS
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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)
|
|
hex view+--------+-------------------------+-------------------------+--------+--------+
|00000000| 54 55 54 4f 52 20 30 36 | fe 2c 00 00 27 01 00 00 |TUTOR 06|.,..'...|
|00000010| 53 65 63 74 69 6f 6e 20 | 32 2e 32 20 20 46 75 6e |Section |2.2 Fun|
|00000020| 63 74 69 6f 6e 73 0d 0a | 00 0d 0b 00 0e 65 32 2d |ctions..|.....e2-|
|00000030| 32 2d 31 0e 47 75 69 64 | 65 64 20 45 78 61 6d 70 |2-1.Guid|ed Examp|
|00000040| 6c 65 20 20 31 0f 20 20 | 54 65 73 74 69 6e 67 20 |le 1. |Testing |
|00000050| 66 6f 72 20 46 75 6e 63 | 74 69 6f 6e 73 20 52 65 |for Func|tions Re|
|00000060| 70 72 65 73 65 6e 74 65 | 64 20 62 79 20 45 71 75 |presente|d by Equ|
|00000070| 61 74 69 6f 6e 73 0d 0a | 00 0d 0b 00 0e 65 32 2d |ations..|.....e2-|
|00000080| 32 2d 32 0e 47 75 69 64 | 65 64 20 45 78 61 6d 70 |2-2.Guid|ed Examp|
|00000090| 6c 65 20 20 32 0f 20 20 | 45 76 61 6c 75 61 74 69 |le 2. |Evaluati|
|000000a0| 6e 67 20 61 20 46 75 6e | 63 74 69 6f 6e 0d 0a 00 |ng a Fun|ction...|
|000000b0| 0d 0b 00 0e 65 32 2d 32 | 2d 33 0e 47 75 69 64 65 |....e2-2|-3.Guide|
|000000c0| 64 20 45 78 61 6d 70 6c | 65 20 20 33 0f 20 20 45 |d Exampl|e 3. E|
|000000d0| 76 61 6c 75 61 74 69 6e | 67 20 61 20 46 75 6e 63 |valuatin|g a Func|
|000000e0| 74 69 6f 6e 0d 0a 00 0d | 0b 00 0e 65 32 2d 32 2d |tion....|...e2-2-|
|000000f0| 34 0e 47 75 69 64 65 64 | 20 45 78 61 6d 70 6c 65 |4.Guided| Example|
|00000100| 20 20 34 0f 20 20 46 69 | 6e 64 69 6e 67 20 74 68 | 4. Fi|nding th|
|00000110| 65 20 44 6f 6d 61 69 6e | 20 6f 66 20 61 20 46 75 |e Domain| of a Fu|
|00000120| 6e 63 74 69 6f 6e 0d 0a | 00 0d 0b 00 0e 65 32 2d |nction..|.....e2-|
|00000130| 32 2d 35 0e 47 75 69 64 | 65 64 20 45 78 61 6d 70 |2-5.Guid|ed Examp|
|00000140| 6c 65 20 20 35 0f 20 20 | 46 69 6e 64 69 6e 67 20 |le 5. |Finding |
|00000150| 61 20 44 69 66 66 65 72 | 65 6e 63 65 20 51 75 6f |a Differ|ence Quo|
|00000160| 74 69 65 6e 74 0d 0a 00 | 0d 0b 00 0e 65 32 2d 32 |tient...|....e2-2|
|00000170| 2d 36 0e 47 75 69 64 65 | 64 20 45 78 61 6d 70 6c |-6.Guide|d Exampl|
|00000180| 65 20 20 36 0f 20 20 41 | 70 70 6c 69 63 61 74 69 |e 6. A|pplicati|
|00000190| 6f 6e 3a 20 56 6f 6c 75 | 6d 65 20 6f 66 20 61 20 |on: Volu|me of a |
|000001a0| 42 6f 78 0d 0a 00 0d 0b | 00 0e 65 32 2d 32 2d 37 |Box.....|..e2-2-7|
|000001b0| 0e 47 75 69 64 65 64 20 | 45 78 61 6d 70 6c 65 20 |.Guided |Example |
|000001c0| 20 37 0f 20 20 41 70 70 | 6c 69 63 61 74 69 6f 6e | 7. App|lication|
|000001d0| 3a 20 52 65 76 65 6e 75 | 65 2c 20 43 6f 73 74 2c |: Revenu|e, Cost,|
|000001e0| 20 61 6e 64 20 50 72 6f | 66 69 74 0d 0a 00 0d 0b | and Pro|fit.....|
|000001f0| 00 0e 69 32 2d 32 2d 31 | 0e 49 6e 74 65 67 72 61 |..i2-2-1|.Integra|
|00000200| 74 65 64 20 45 78 61 6d | 70 6c 65 20 20 31 0f 20 |ted Exam|ple 1. |
|00000210| 20 46 69 6e 64 69 6e 67 | 20 74 68 65 20 5a 65 72 | Finding| the Zer|
|00000220| 6f 73 20 6f 66 20 61 20 | 46 75 6e 63 74 69 6f 6e |os of a |Function|
|00000230| 0d 0a 00 0d 0b 00 0e 69 | 32 2d 32 2d 32 0e 49 6e |.......i|2-2-2.In|
|00000240| 74 65 67 72 61 74 65 64 | 20 45 78 61 6d 70 6c 65 |tegrated| Example|
|00000250| 20 20 32 0f 20 20 57 72 | 69 74 69 6e 67 20 61 20 | 2. Wr|iting a |
|00000260| 53 65 74 20 6f 66 20 4f | 72 64 65 72 65 64 20 50 |Set of O|rdered P|
|00000270| 61 69 72 73 20 66 6f 72 | 20 61 20 46 75 6e 63 74 |airs for| a Funct|
|00000280| 69 6f 6e 0d 0a 00 0d 0b | 00 0e 69 32 2d 32 2d 33 |ion.....|..i2-2-3|
|00000290| 0e 49 6e 74 65 67 72 61 | 74 65 64 20 45 78 61 6d |.Integra|ted Exam|
|000002a0| 70 6c 65 20 20 33 0f 20 | 20 53 65 74 74 69 6e 67 |ple 3. | Setting|
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|000002e0| 20 20 46 75 6e 63 74 69 | 6f 6e 73 0d 0b 00 44 65 | Functi|ons...De|
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|00000390| 20 20 11 31 3d 20 11 33 | 78 20 20 20 20 20 20 20 | .1= .3|x |
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|000003b0| 20 11 31 3d 20 11 34 53 | 20 11 31 32 11 33 78 20 | .1= .4S| .12.3x |
|000003c0| 11 31 2d 20 31 20 20 20 | 20 20 20 20 20 20 20 20 |.1- 1 | |
|000003d0| 20 28 63 29 20 20 11 33 | 78 20 20 11 31 2d 20 11 | (c) .3|x .1- .|
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|00000430| 31 69 73 20 61 20 66 75 | 6e 63 74 69 6f 6e 20 6f |1is a fu|nction o|
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|000004c0| 20 20 20 20 20 20 20 20 | 20 11 32 32 0d 0b 00 20 | | .22... |
|000004d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000004e0| 11 33 79 20 20 11 31 3d | 20 11 33 78 20 20 20 20 |.3y .1=| .3x |
|000004f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000500| 20 11 31 12 31 11 32 47 | 69 76 65 6e 20 65 71 75 | .1.1.2G|iven equ|
|00000510| 61 74 69 6f 6e 11 31 12 | 30 13 0d 0a 00 20 20 20 |ation.1.|0.... |
|00000520| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000530| 20 20 20 20 20 11 34 44 | 32 0d 0b 00 20 20 20 20 | .4D|2... |
|00000540| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 33 | | .3|
|00000550| 79 20 11 31 3d 20 11 34 | 2b 53 20 11 33 78 20 20 |y .1= .4|+S .3x |
|00000560| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000570| 11 31 12 31 11 32 53 6f | 6c 76 65 20 66 6f 72 20 |.1.1.2So|lve for |
|00000580| 79 11 31 12 30 13 0d 0a | 00 0d 0b 00 20 20 20 20 |y.1.0...|.... |
|00000590| 54 68 65 20 11 34 2b 20 | 11 31 69 6e 64 69 63 61 |The .4+ |.1indica|
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|000005b0| 68 20 76 61 6c 75 65 20 | 6f 66 20 11 33 78 11 31 |h value |of .3x.1|
|000005c0| 2c 20 74 68 65 72 65 20 | 63 6f 72 72 65 73 70 6f |, there |correspo|
|000005d0| 6e 64 73 20 74 77 6f 20 | 76 61 6c 75 65 73 20 6f |nds two |values o|
|000005e0| 66 0d 0a 00 20 20 20 20 | 11 33 79 11 31 2e 20 20 |f... |.3y.1. |
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|00000610| 6f 6e 20 6f 66 20 11 33 | 78 11 31 2e 13 0d 0a 00 |on of .3|x.1.....|
|00000620| 0d 0b 00 62 29 20 20 54 | 68 69 73 20 65 71 75 61 |...b) T|his equa|
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|00000650| 2e 0d 0a 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |.... | |
|00000660| 20 20 20 20 20 20 20 20 | 20 20 20 11 34 44 32 32 | | .4D22|
|00000670| 32 32 32 32 0d 0b 00 20 | 20 20 20 20 20 20 20 20 |2222... | |
|00000680| 20 20 20 20 20 20 20 20 | 20 11 33 79 20 11 31 3d | | .3y .1=|
|00000690| 20 11 34 53 20 11 31 32 | 11 33 78 20 11 31 2d 20 | .4S .12|.3x .1- |
|000006a0| 31 13 0d 0a 00 0d 0b 00 | 20 20 20 20 49 6e 20 74 |1.......| In t|
|000006b0| 68 69 73 20 63 61 73 65 | 2c 20 66 6f 72 20 65 61 |his case|, for ea|
|000006c0| 63 68 20 76 61 6c 75 65 | 20 6f 66 20 11 33 78 11 |ch value| of .3x.|
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|00000700| 20 20 20 20 54 68 65 72 | 65 66 6f 72 65 2c 20 11 | Ther|efore, .|
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|00000720| 6f 6e 20 6f 66 20 11 33 | 78 11 31 2e 13 0d 0a 00 |on of .3|x.1.....|
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|000007d0| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
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|000007f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 | | .|
|00000800| 31 12 31 20 20 20 20 20 | 20 20 20 20 20 11 32 32 |1.1 | .22|
|00000810| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000820| 11 31 12 30 0d 0b 00 20 | 20 20 20 20 20 20 20 20 |.1.0... | |
|00000830| 20 20 20 20 20 20 20 11 | 33 78 20 79 20 11 31 2d | .|3x y .1-|
|00000840| 20 11 33 79 20 11 31 3d | 20 2d 11 33 78 20 20 20 | .3y .1=| -.3x |
|00000850| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 11 31 12 | | .1.|
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|00000870| 72 6f 6d 20 62 6f 74 68 | 20 73 69 64 65 73 11 31 |rom both| sides.1|
|00000880| 12 30 13 0d 0a 00 20 20 | 20 20 20 20 20 20 20 20 |.0.... | |
|00000890| 20 20 20 20 20 20 20 11 | 32 32 20 20 20 20 20 20 | .|22 |
|000008a0| 20 20 20 20 32 0d 0b 00 | 20 20 20 20 20 20 20 20 | 2...| |
|000008b0| 20 20 20 20 20 20 11 33 | 79 11 31 28 11 33 78 20 | .3|y.1(.3x |
|000008c0| 20 11 31 2d 20 31 29 20 | 3d 20 2d 11 33 78 20 20 | .1- 1) |= -.3x |
|000008d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 31 | | .1|
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|00000900| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000910| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 | | .|
|00000920| 32 32 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 |22... | |
|00000930| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000940| 20 20 20 11 33 78 0d 0b | 00 20 20 20 20 20 20 20 | .3x..|. |
|00000950| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 79 | | y|
|00000960| 20 11 31 3d 20 2d 11 34 | 32 32 32 32 32 32 20 20 | .1= -.4|222222 |
|00000970| 20 20 20 20 20 20 20 20 | 20 11 31 12 31 11 32 53 | | .1.1.2S|
|00000980| 6f 6c 76 65 20 66 6f 72 | 20 79 11 31 12 30 0d 0b |olve for| y.1.0..|
|00000990| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
|000009a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 11 32 32 | | .22|
|000009b0| 0d 0b 00 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |... | |
|000009c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 33 | | .3|
|000009d0| 78 20 20 11 31 2d 20 31 | 0d 0a 00 20 20 20 20 49 |x .1- 1|... I|
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|00000a00| 33 78 11 31 2c 20 74 68 | 65 72 65 20 63 6f 72 72 |3x.1, th|ere corr|
|00000a10| 65 73 70 6f 6e 64 20 6f | 6e 6c 79 20 6f 6e 65 20 |espond o|nly one |
|00000a20| 76 61 6c 75 65 20 6f 66 | 20 11 33 79 11 31 2e 0d |value of| .3y.1..|
|00000a30| 0a 00 20 20 20 20 54 68 | 65 72 65 66 6f 72 65 2c |.. Th|erefore,|
|00000a40| 20 11 33 79 20 11 31 69 | 73 20 61 20 66 75 6e 63 | .3y .1i|s a func|
|00000a50| 74 69 6f 6e 20 6f 66 20 | 11 33 78 11 31 2e 0d 0a |tion of |.3x.1...|
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|00000a70| 6e 63 74 69 6f 6e 73 0d | 0b 00 20 20 20 20 20 20 |nctions.|.. |
|00000a80| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000a90| 20 20 20 20 20 20 20 20 | 20 11 32 32 0d 0b 00 11 | | .22....|
|00000aa0| 31 45 76 61 6c 75 61 74 | 65 20 74 68 65 20 66 75 |1Evaluat|e the fu|
|00000ab0| 6e 63 74 69 6f 6e 20 11 | 33 66 11 31 28 11 33 78 |nction .|3f.1(.3x|
|00000ac0| 11 31 29 20 3d 20 32 11 | 33 78 20 20 11 31 2d 20 |.1) = 2.|3x .1- |
|00000ad0| 33 11 33 78 20 11 31 2b | 20 34 20 77 68 65 6e 20 |3.3x .1+| 4 when |
|00000ae0| 11 33 78 20 11 31 3d 20 | 2d 31 2c 20 30 2c 20 61 |.3x .1= |-1, 0, a|
|00000af0| 6e 64 20 11 33 78 20 11 | 31 2b 20 31 2e 0d 0a 00 |nd .3x .|1+ 1....|
|00000b00| 0d 0b 00 13 12 31 53 4f | 4c 55 54 49 4f 4e 12 30 |.....1SO|LUTION.0|
|00000b10| 0d 0a 00 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |... | |
|00000b20| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000b30| 20 20 20 11 32 32 0d 0b | 00 11 31 52 65 70 6c 61 | .22..|..1Repla|
|00000b40| 63 69 6e 67 20 11 33 78 | 20 11 31 77 69 74 68 20 |cing .3x| .1with |
|00000b50| 2d 31 20 69 6e 20 11 33 | 66 11 31 28 11 33 78 11 |-1 in .3|f.1(.3x.|
|00000b60| 31 29 20 3d 20 32 11 33 | 78 20 20 11 31 2d 20 33 |1) = 2.3|x .1- 3|
|00000b70| 11 33 78 20 11 31 2b 20 | 34 20 79 69 65 6c 64 73 |.3x .1+ |4 yields|
|00000b80| 20 74 68 65 20 66 6f 6c | 6c 6f 77 69 6e 67 2e 0d | the fol|lowing..|
|00000b90| 0a 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.. | |
|00000ba0| 20 20 20 20 20 20 20 20 | 20 11 32 32 0d 0b 00 20 | | .22... |
|00000bb0| 20 20 20 20 20 20 20 20 | 20 11 33 66 11 31 28 2d | | .3f.1(-|
|00000bc0| 31 29 20 3d 20 32 28 2d | 31 29 20 20 2d 20 33 28 |1) = 2(-|1) - 3(|
|00000bd0| 2d 31 29 20 2b 20 34 20 | 3d 20 32 20 2b 20 33 20 |-1) + 4 |= 2 + 3 |
|00000be0| 2b 20 34 20 3d 20 39 13 | 0d 0a 00 20 20 20 20 20 |+ 4 = 9.|... |
|00000bf0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000c00| 20 20 20 20 20 20 20 20 | 20 20 11 32 32 0d 0b 00 | | .22...|
|00000c10| 11 31 52 65 70 6c 61 63 | 69 6e 67 20 11 33 78 20 |.1Replac|ing .3x |
|00000c20| 11 31 77 69 74 68 20 30 | 20 69 6e 20 11 33 66 11 |.1with 0| in .3f.|
|00000c30| 31 28 11 33 78 11 31 29 | 20 3d 20 32 11 33 78 20 |1(.3x.1)| = 2.3x |
|00000c40| 20 11 31 2d 20 33 11 33 | 78 20 11 31 2b 20 34 20 | .1- 3.3|x .1+ 4 |
|00000c50| 79 69 65 6c 64 73 20 74 | 68 65 20 66 6f 6c 6c 6f |yields t|he follo|
|00000c60| 77 69 6e 67 2e 0d 0a 00 | 20 20 20 20 20 20 20 20 |wing....| |
|00000c70| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 32 | | .2|
|00000c80| 32 0d 0b 00 20 20 20 20 | 20 20 20 20 20 20 20 11 |2... | .|
|00000c90| 33 66 11 31 28 30 29 20 | 3d 20 32 28 30 29 20 20 |3f.1(0) |= 2(0) |
|00000ca0| 2d 20 33 28 30 29 20 2b | 20 34 20 3d 20 30 20 2b |- 3(0) +| 4 = 0 +|
|00000cb0| 20 30 20 2b 20 34 20 3d | 20 34 13 0d 0a 00 20 20 | 0 + 4 =| 4.... |
|00000cc0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000cd0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000ce0| 20 11 32 32 0d 0b 00 11 | 31 52 65 70 6c 61 63 69 | .22....|1Replaci|
|00000cf0| 6e 67 20 11 33 78 20 11 | 31 77 69 74 68 20 11 33 |ng .3x .|1with .3|
|00000d00| 78 20 11 31 2b 20 31 20 | 69 6e 20 11 33 66 11 31 |x .1+ 1 |in .3f.1|
|00000d10| 28 11 33 78 11 31 29 20 | 3d 20 32 11 33 78 20 20 |(.3x.1) |= 2.3x |
|00000d20| 11 31 2d 20 33 11 33 78 | 20 11 31 2b 20 34 20 79 |.1- 3.3x| .1+ 4 y|
|00000d30| 69 65 6c 64 73 20 74 68 | 65 20 66 6f 6c 6c 6f 77 |ields th|e follow|
|00000d40| 69 6e 67 2e 0d 0a 00 20 | 20 20 20 20 20 20 20 20 |ing.... | |
|00000d50| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000d60| 20 11 32 32 0d 0b 00 20 | 20 20 20 20 20 20 11 33 | .22... | .3|
|00000d70| 66 11 31 28 11 33 78 20 | 11 31 2b 20 31 29 20 3d |f.1(.3x |.1+ 1) =|
|00000d80| 20 32 28 11 33 78 20 11 | 31 2b 20 31 29 20 20 2d | 2(.3x .|1+ 1) -|
|00000d90| 20 33 28 11 33 78 20 11 | 31 2b 20 31 29 20 2b 20 | 3(.3x .|1+ 1) + |
|00000da0| 34 13 0d 0a 00 20 20 20 | 20 20 20 20 20 20 20 20 |4.... | |
|00000db0| 20 20 20 20 20 20 20 20 | 20 20 11 32 32 0d 0b 00 | | .22...|
|00000dc0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000dd0| 11 31 3d 20 32 28 11 33 | 78 20 20 11 31 2b 20 32 |.1= 2(.3|x .1+ 2|
|00000de0| 11 33 78 20 11 31 2b 20 | 31 29 20 2d 20 33 11 33 |.3x .1+ |1) - 3.3|
|00000df0| 78 20 11 31 2d 20 33 20 | 2b 20 34 13 0d 0a 00 20 |x .1- 3 |+ 4.... |
|00000e00| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000e10| 20 20 20 11 32 32 0d 0b | 00 20 20 20 20 20 20 20 | .22..|. |
|00000e20| 20 20 20 20 20 20 20 20 | 20 11 31 3d 20 32 11 33 | | .1= 2.3|
|00000e30| 78 20 20 11 31 2b 20 34 | 11 33 78 20 11 31 2b 20 |x .1+ 4|.3x .1+ |
|00000e40| 32 20 2d 20 33 11 33 78 | 20 11 31 2b 20 31 13 0d |2 - 3.3x| .1+ 1..|
|00000e50| 0a 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.. | |
|00000e60| 20 20 20 20 20 20 11 32 | 32 0d 0b 00 20 20 20 20 | .2|2... |
|00000e70| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 31 3d 20 | | .1= |
|00000e80| 32 11 33 78 20 20 11 31 | 2b 20 11 33 78 20 11 31 |2.3x .1|+ .3x .1|
|00000e90| 2b 20 33 0d 0a 00 53 65 | 63 74 69 6f 6e 20 32 2e |+ 3...Se|ction 2.|
|00000ea0| 32 20 20 46 75 6e 63 74 | 69 6f 6e 73 0d 0b 00 45 |2 Funct|ions...E|
|00000eb0| 76 61 6c 75 61 74 65 20 | 74 68 65 20 66 75 6e 63 |valuate |the func|
|00000ec0| 74 69 6f 6e 20 11 33 66 | 11 31 28 11 33 78 11 31 |tion .3f|.1(.3x.1|
|00000ed0| 29 20 3d 20 7c 2d 32 11 | 33 78 11 31 7c 20 77 68 |) = |-2.|3x.1| wh|
|00000ee0| 65 6e 20 11 33 78 20 11 | 31 3d 20 2d 31 2c 20 33 |en .3x .|1= -1, 3|
|00000ef0| 2c 20 61 6e 64 20 11 33 | 78 20 11 31 2d 20 31 2e |, and .3|x .1- 1.|
|00000f00| 0d 0a 00 0d 0b 00 13 12 | 31 53 4f 4c 55 54 49 4f |........|1SOLUTIO|
|00000f10| 4e 12 30 0d 0a 00 0d 0b | 00 52 65 70 6c 61 63 69 |N.0.....|.Replaci|
|00000f20| 6e 67 20 11 33 78 20 11 | 31 77 69 74 68 20 2d 31 |ng .3x .|1with -1|
|00000f30| 20 69 6e 20 11 33 66 11 | 31 28 11 33 78 11 31 29 | in .3f.|1(.3x.1)|
|00000f40| 20 3d 20 7c 2d 32 11 33 | 78 11 31 7c 20 79 69 65 | = |-2.3|x.1| yie|
|00000f50| 6c 64 73 20 74 68 65 20 | 66 6f 6c 6c 6f 77 69 6e |lds the |followin|
|00000f60| 67 2e 0d 0a 00 0d 0b 00 | 20 20 20 20 20 20 20 20 |g.......| |
|00000f70| 20 20 20 11 33 66 11 31 | 28 2d 31 29 20 3d 20 7c | .3f.1|(-1) = ||
|00000f80| 2d 32 28 2d 31 29 7c 20 | 3d 20 7c 32 7c 20 3d 20 |-2(-1)| |= |2| = |
|00000f90| 32 13 0d 0a 00 0d 0b 00 | 52 65 70 6c 61 63 69 6e |2.......|Replacin|
|00000fa0| 67 20 11 33 78 20 11 31 | 77 69 74 68 20 33 20 69 |g .3x .1|with 3 i|
|00000fb0| 6e 20 11 33 66 11 31 28 | 11 33 78 11 31 29 20 3d |n .3f.1(|.3x.1) =|
|00000fc0| 20 7c 2d 32 11 33 78 11 | 31 7c 20 79 69 65 6c 64 | |-2.3x.|1| yield|
|00000fd0| 73 20 74 68 65 20 66 6f | 6c 6c 6f 77 69 6e 67 2e |s the fo|llowing.|
|00000fe0| 0d 0a 00 0d 0b 00 20 20 | 20 20 20 20 20 20 20 20 |...... | |
|00000ff0| 20 20 11 33 66 11 31 28 | 33 29 20 3d 20 7c 2d 32 | .3f.1(|3) = |-2|
|00001000| 28 33 29 7c 20 3d 20 7c | 2d 36 7c 20 3d 20 36 13 |(3)| = ||-6| = 6.|
|00001010| 0d 0a 00 0d 0b 00 52 65 | 70 6c 61 63 69 6e 67 20 |......Re|placing |
|00001020| 11 33 78 20 11 31 77 69 | 74 68 20 11 33 78 20 11 |.3x .1wi|th .3x .|
|00001030| 31 2d 20 31 20 69 6e 20 | 11 33 66 11 31 28 11 33 |1- 1 in |.3f.1(.3|
|00001040| 78 11 31 29 20 3d 20 7c | 2d 32 11 33 78 11 31 7c |x.1) = ||-2.3x.1||
|00001050| 20 79 69 65 6c 64 73 20 | 74 68 65 20 66 6f 6c 6c | yields |the foll|
|00001060| 6f 77 69 6e 67 2e 0d 0a | 00 0d 0b 00 20 20 20 20 |owing...|.... |
|00001070| 20 20 20 20 11 33 66 11 | 31 28 11 33 78 20 11 31 | .3f.|1(.3x .1|
|00001080| 2d 20 31 29 20 3d 20 7c | 2d 32 28 11 33 78 20 11 |- 1) = ||-2(.3x .|
|00001090| 31 2d 20 31 29 7c 20 3d | 20 7c 2d 32 11 33 78 20 |1- 1)| =| |-2.3x |
|000010a0| 11 31 2b 20 32 7c 0d 0a | 00 53 65 63 74 69 6f 6e |.1+ 2|..|.Section|
|000010b0| 20 32 2e 32 20 20 46 75 | 6e 63 74 69 6f 6e 73 0d | 2.2 Fu|nctions.|
|000010c0| 0b 00 46 69 6e 64 20 74 | 68 65 20 64 6f 6d 61 69 |..Find t|he domai|
|000010d0| 6e 20 6f 66 20 74 68 65 | 20 66 6f 6c 6c 6f 77 69 |n of the| followi|
|000010e0| 6e 67 20 66 75 6e 63 74 | 69 6f 6e 73 2e 0d 0a 00 |ng funct|ions....|
|000010f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 33 | | .3|
|00001100| 78 20 11 31 2d 20 34 20 | 20 20 20 20 20 20 20 20 |x .1- 4 | |
|00001110| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001120| 20 20 20 20 20 20 20 20 | 20 20 20 11 33 74 0d 0b | | .3t..|
|00001130| 00 11 31 28 61 29 20 20 | 11 33 68 11 31 28 11 33 |..1(a) |.3h.1(.3|
|00001140| 78 11 31 29 20 3d 20 11 | 34 32 32 32 32 32 32 32 |x.1) = .|42222222|
|00001150| 32 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |2 | |
|00001160| 20 20 20 20 20 11 31 28 | 62 29 20 20 11 33 66 11 | .1(|b) .3f.|
|00001170| 31 28 11 33 74 11 31 29 | 20 3d 20 11 34 32 32 32 |1(.3t.1)| = .4222|
|00001180| 32 32 32 32 0d 0b 00 20 | 20 20 20 20 20 20 20 20 |2222... | |
|00001190| 20 20 20 11 33 78 11 31 | 28 11 33 78 20 11 31 2d | .3x.1|(.3x .1-|
|000011a0| 20 31 29 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | 1) | |
|000011b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000011c0| 20 20 20 20 11 34 44 32 | 32 32 32 32 0d 0b 00 20 | .4D2|2222... |
|000011d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000011e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000011f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001200| 20 20 20 53 20 11 31 33 | 20 2d 20 11 33 74 0d 0a | S .13| - .3t..|
|00001210| 00 11 31 13 12 31 53 4f | 4c 55 54 49 4f 4e 12 30 |..1..1SO|LUTION.0|
|00001220| 0d 0a 00 61 29 20 20 46 | 6f 72 20 74 68 69 73 20 |...a) F|or this |
|00001230| 66 75 6e 63 74 69 6f 6e | 2c 20 77 65 20 65 78 63 |function|, we exc|
|00001240| 6c 75 64 65 20 61 6c 6c | 20 76 61 6c 75 65 73 20 |lude all| values |
|00001250| 6f 66 20 11 33 78 20 11 | 31 66 6f 72 20 77 68 69 |of .3x .|1for whi|
|00001260| 63 68 20 74 68 65 20 64 | 65 6e 6f 6d 69 6e 61 74 |ch the d|enominat|
|00001270| 6f 72 20 69 73 0d 0a 00 | 20 20 20 20 7a 65 72 6f |or is...| zero|
|00001280| 2e 0d 0a 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |.... | |
|00001290| 20 11 33 78 11 31 28 11 | 33 78 20 11 31 2d 20 31 | .3x.1(.|3x .1- 1|
|000012a0| 29 20 3d 20 30 20 20 20 | 20 11 34 35 35 36 20 20 |) = 0 | .4556 |
|000012b0| 20 20 11 33 78 20 11 31 | 3d 20 30 2c 20 11 33 78 | .3x .1|= 0, .3x|
|000012c0| 20 11 31 3d 20 31 20 20 | 20 20 20 20 20 20 20 20 | .1= 1 | |
|000012d0| 12 31 11 32 45 78 63 6c | 75 64 65 64 20 76 61 6c |.1.2Excl|uded val|
|000012e0| 75 65 73 11 31 12 30 13 | 0d 0a 00 0d 0b 00 20 20 |ues.1.0.|...... |
|000012f0| 20 20 54 68 75 73 2c 20 | 74 68 65 20 64 6f 6d 61 | Thus, |the doma|
|00001300| 69 6e 20 6f 66 20 11 33 | 68 20 11 31 63 6f 6e 73 |in of .3|h .1cons|
|00001310| 69 73 74 73 20 6f 66 20 | 61 6c 6c 20 72 65 61 6c |ists of |all real|
|00001320| 20 76 61 6c 75 65 73 20 | 6f 66 20 11 33 78 20 11 | values |of .3x .|
|00001330| 31 73 75 63 68 20 74 68 | 61 74 20 11 33 78 20 11 |1such th|at .3x .|
|00001340| 34 3d 20 11 31 30 20 61 | 6e 64 0d 0a 00 20 20 20 |4= .10 a|nd... |
|00001350| 20 11 33 78 20 11 34 3d | 20 11 31 31 2e 13 0d 0a | .3x .4=| .11....|
|00001360| 00 0d 0b 00 62 29 20 20 | 46 6f 72 20 74 68 69 73 |....b) |For this|
|00001370| 20 66 75 6e 63 74 69 6f | 6e 2c 20 77 65 20 6d 75 | functio|n, we mu|
|00001380| 73 74 20 65 78 63 6c 75 | 64 65 20 61 6c 6c 20 76 |st exclu|de all v|
|00001390| 61 6c 75 65 73 20 6f 66 | 20 11 33 74 20 11 31 66 |alues of| .3t .1f|
|000013a0| 6f 72 20 77 68 69 63 68 | 20 74 68 65 20 0d 0a 00 |or which| the ...|
|000013b0| 20 20 20 20 64 65 6e 6f | 6d 69 6e 61 74 6f 72 20 | deno|minator |
|000013c0| 69 73 20 7a 65 72 6f 2c | 20 61 73 20 77 65 6c 6c |is zero,| as well|
|000013d0| 20 61 73 20 74 68 6f 73 | 65 20 76 61 6c 75 65 73 | as thos|e values|
|000013e0| 20 66 6f 72 20 77 68 69 | 63 68 20 74 68 65 20 72 | for whi|ch the r|
|000013f0| 61 64 69 63 61 6e 64 0d | 0a 00 20 20 20 20 28 33 |adicand.|.. (3|
|00001400| 20 2d 20 11 33 74 11 31 | 29 20 69 73 20 6e 65 67 | - .3t.1|) is neg|
|00001410| 61 74 69 76 65 2e 0d 0a | 00 0d 0b 00 20 20 20 20 |ative...|.... |
|00001420| 20 20 20 20 20 20 20 20 | 20 20 20 20 33 20 2d 20 | | 3 - |
|00001430| 11 33 74 20 11 34 3c 20 | 11 31 30 20 20 20 20 11 |.3t .4< |.10 .|
|00001440| 34 35 35 36 20 20 20 20 | 11 33 74 20 11 34 3e 20 |4556 |.3t .4> |
|00001450| 11 31 33 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.13 | |
|00001460| 12 31 11 32 45 78 63 6c | 75 64 65 64 20 76 61 6c |.1.2Excl|uded val|
|00001470| 75 65 73 11 31 12 30 13 | 0d 0a 00 0d 0b 00 20 20 |ues.1.0.|...... |
|00001480| 20 20 54 68 75 73 2c 20 | 74 68 65 20 64 6f 6d 61 | Thus, |the doma|
|00001490| 69 6e 20 6f 66 20 11 33 | 66 20 11 31 63 6f 6e 73 |in of .3|f .1cons|
|000014a0| 69 73 74 73 20 6f 66 20 | 61 6c 6c 20 72 65 61 6c |ists of |all real|
|000014b0| 20 76 61 6c 75 65 73 20 | 6f 66 20 11 33 74 20 11 | values |of .3t .|
|000014c0| 31 73 75 63 68 20 74 68 | 61 74 20 11 33 74 20 11 |1such th|at .3t .|
|000014d0| 31 3c 20 33 2e 0d 0a 00 | 53 65 63 74 69 6f 6e 20 |1< 3....|Section |
|000014e0| 32 2e 32 20 20 46 75 6e | 63 74 69 6f 6e 73 0d 0b |2.2 Fun|ctions..|
|000014f0| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 11 32 32 |. | .22|
|00001500| 0d 0b 00 11 31 4c 65 74 | 20 11 33 66 11 31 28 11 |....1Let| .3f.1(.|
|00001510| 33 78 11 31 29 20 3d 20 | 11 33 78 20 20 11 31 2b |3x.1) = |.3x .1+|
|00001520| 20 32 11 33 78 20 11 31 | 2d 20 31 2e 20 20 46 6f | 2.3x .1|- 1. Fo|
|00001530| 72 20 74 68 69 73 20 66 | 75 6e 63 74 69 6f 6e 2c |r this f|unction,|
|00001540| 20 65 76 61 6c 75 61 74 | 65 20 74 68 65 20 66 6f | evaluat|e the fo|
|00001550| 6c 6c 6f 77 69 6e 67 20 | 0d 0a 00 64 69 66 66 65 |llowing |...diffe|
|00001560| 72 65 6e 63 65 20 71 75 | 6f 74 69 65 6e 74 20 61 |rence qu|otient a|
|00001570| 6e 64 20 73 69 6d 70 6c | 69 66 79 20 79 6f 75 72 |nd simpl|ify your|
|00001580| 20 61 6e 73 77 65 72 2e | 0d 0a 00 0d 0b 00 20 20 | answer.|...... |
|00001590| 20 20 20 11 33 66 11 31 | 28 11 33 78 20 11 31 2b | .3f.1|(.3x .1+|
|000015a0| 20 11 34 64 11 33 78 11 | 31 29 20 2d 20 11 33 66 | .4d.3x.|1) - .3f|
|000015b0| 11 31 28 11 33 78 11 31 | 29 0d 0b 00 20 20 20 20 |.1(.3x.1|)... |
|000015c0| 20 11 34 32 32 32 32 32 | 32 32 32 32 32 32 32 32 | .422222|22222222|
|000015d0| 32 32 32 0d 0b 00 20 20 | 20 20 20 20 20 20 20 20 |222... | |
|000015e0| 20 20 64 11 33 78 0d 0a | 00 11 31 13 12 31 53 4f | d.3x..|..1..1SO|
|000015f0| 4c 55 54 49 4f 4e 12 30 | 0d 0b 00 20 20 20 20 20 |LUTION.0|... |
|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 11 32 32 20 20 | | .22 |
|00001620| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001630| 20 20 20 32 0d 0b 00 20 | 20 20 20 20 11 33 66 11 | 2... | .3f.|
|00001640| 31 28 11 33 78 20 11 31 | 2b 20 11 34 64 11 33 78 |1(.3x .1|+ .4d.3x|
|00001650| 11 31 29 20 2d 20 11 33 | 66 11 31 28 11 33 78 11 |.1) - .3|f.1(.3x.|
|00001660| 31 29 20 20 20 28 11 33 | 78 20 11 31 2b 20 11 34 |1) (.3|x .1+ .4|
|00001670| 64 11 33 78 11 31 29 20 | 20 2b 20 32 28 11 33 78 |d.3x.1) | + 2(.3x|
|00001680| 20 11 31 2b 20 11 34 64 | 11 33 78 11 31 29 20 2d | .1+ .4d|.3x.1) -|
|00001690| 20 31 20 2d 20 28 78 20 | 20 2b 20 32 11 33 78 20 | 1 - (x | + 2.3x |
|000016a0| 11 31 2d 20 31 29 0d 0b | 00 20 20 20 20 20 11 34 |.1- 1)..|. .4|
|000016b0| 32 32 32 32 32 32 32 32 | 32 32 32 32 32 32 32 32 |22222222|22222222|
|000016c0| 20 11 31 3d 20 11 34 32 | 32 32 32 32 32 32 32 32 | .1= .42|22222222|
|000016d0| 32 32 32 32 32 32 32 32 | 32 32 32 32 32 32 32 32 |22222222|22222222|
|000016e0| 32 32 32 32 32 32 32 32 | 32 32 32 32 32 32 32 32 |22222222|22222222|
|000016f0| 0d 0b 00 20 20 20 20 20 | 20 20 20 20 20 20 20 64 |... | d|
|00001700| 11 33 78 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.3x | |
|00001710| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 11 34 64 | | .4d|
|00001720| 11 33 78 13 0d 0a 00 20 | 20 20 20 20 20 20 20 20 |.3x.... | |
|00001730| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001740| 11 32 32 20 20 20 20 20 | 20 20 20 20 20 20 20 32 |.22 | 2|
|00001750| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001760| 20 20 20 32 0d 0b 00 20 | 20 20 20 20 20 20 20 20 | 2... | |
|00001770| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 | | .|
|00001780| 33 78 20 20 11 31 2b 20 | 32 11 33 78 11 34 64 11 |3x .1+ |2.3x.4d.|
|00001790| 33 78 20 11 31 2b 20 11 | 34 64 11 33 78 20 20 11 |3x .1+ .|4d.3x .|
|000017a0| 31 2b 20 32 11 33 78 20 | 11 31 2b 20 32 11 34 64 |1+ 2.3x |.1+ 2.4d|
|000017b0| 11 31 78 20 2d 20 31 20 | 2d 20 11 33 78 20 20 11 |.1x - 1 |- .3x .|
|000017c0| 31 2d 20 32 11 33 78 20 | 11 31 2b 20 31 0d 0b 00 |1- 2.3x |.1+ 1...|
|000017d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000017e0| 20 20 20 20 20 20 3d 20 | 11 34 32 32 32 32 32 32 | = |.4222222|
|000017f0| 32 32 32 32 32 32 32 32 | 32 32 32 32 32 32 32 32 |22222222|22222222|
|00001800| 32 32 32 32 32 32 32 32 | 32 32 32 32 32 32 32 32 |22222222|22222222|
|00001810| 32 32 32 32 32 32 0d 0b | 00 20 20 20 20 20 20 20 |222222..|. |
|00001820| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001830| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001840| 20 20 20 64 11 33 78 13 | 0d 0a 00 20 20 20 20 20 | d.3x.|... |
|00001850| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001860| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 32 32 0d | | .22.|
|00001870| 0b 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.. | |
|00001880| 20 20 20 20 20 20 20 20 | 20 20 11 31 32 11 33 78 | | .12.3x|
|00001890| 11 34 64 11 33 78 20 11 | 31 2b 20 11 34 64 11 33 |.4d.3x .|1+ .4d.3|
|000018a0| 78 20 20 11 31 2b 20 32 | 11 34 64 11 33 78 0d 0b |x .1+ 2|.4d.3x..|
|000018b0| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
|000018c0| 20 20 20 20 20 20 20 11 | 31 3d 20 11 34 32 32 32 | .|1= .4222|
|000018d0| 32 32 32 32 32 32 32 32 | 32 32 32 32 32 0d 0b 00 |22222222|22222...|
|000018e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000018f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 64 11 | | d.|
|00001900| 33 78 13 0d 0a 00 0d 0b | 00 20 20 20 20 20 20 20 |3x......|. |
|00001910| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001920| 20 11 34 64 11 33 78 11 | 31 28 32 11 33 78 20 11 | .4d.3x.|1(2.3x .|
|00001930| 31 2b 20 11 34 64 11 33 | 78 20 11 31 2b 20 32 29 |1+ .4d.3|x .1+ 2)|
|00001940| 0d 0b 00 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |... | |
|00001950| 20 20 20 20 20 20 20 20 | 20 3d 20 11 34 32 32 32 | | = .4222|
|00001960| 32 32 32 32 32 32 32 32 | 32 32 32 32 0d 0b 00 20 |22222222|2222... |
|00001970| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001980| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 64 11 33 | | d.3|
|00001990| 78 13 0d 0a 00 0d 0a 00 | 20 20 20 20 20 20 20 20 |x.......| |
|000019a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 31 | | .1|
|000019b0| 3d 20 32 11 33 78 20 11 | 31 2b 20 11 34 64 11 33 |= 2.3x .|1+ .4d.3|
|000019c0| 78 20 11 31 2b 20 32 0d | 0a 00 53 65 63 74 69 6f |x .1+ 2.|..Sectio|
|000019d0| 6e 20 32 2e 32 20 20 46 | 75 6e 63 74 69 6f 6e 73 |n 2.2 F|unctions|
|000019e0| 41 6e 20 6f 70 65 6e 20 | 62 6f 78 20 69 73 20 74 |An open |box is t|
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|00001a00| 20 73 71 75 61 72 65 0d | 0b 00 20 20 20 20 20 20 | square.|.. |
|00001a10| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001a20| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001a30| 20 20 20 20 14 6b 33 2d | 34 2d 39 2e 6d 14 34 31 | .k3-|4-9.m.41|
|00001a40| 14 30 14 36 30 14 38 14 | 0d 0b 00 70 69 65 63 65 |.0.60.8.|...piece|
|00001a50| 20 6f 66 20 6d 61 74 65 | 72 69 61 6c 20 31 36 20 | of mate|rial 16 |
|00001a60| 69 6e 63 68 65 73 20 6f | 6e 20 61 20 73 69 64 65 |inches o|n a side|
|00001a70| 0d 0a 00 62 79 20 63 75 | 74 74 69 6e 67 20 65 71 |...by cu|tting eq|
|00001a80| 75 61 6c 20 73 71 75 61 | 72 65 73 20 66 72 6f 6d |ual squa|res from|
|00001a90| 20 65 61 63 68 0d 0a 00 | 63 6f 72 6e 65 72 20 61 | each...|corner a|
|00001aa0| 6e 64 20 74 75 72 6e 69 | 6e 67 20 75 70 20 74 68 |nd turni|ng up th|
|00001ab0| 65 20 73 69 64 65 73 20 | 28 73 65 65 0d 0a 00 66 |e sides |(see...f|
|00001ac0| 69 67 75 72 65 29 2e 20 | 20 57 72 69 74 65 20 74 |igure). | Write t|
|00001ad0| 68 65 20 76 6f 6c 75 6d | 65 20 11 33 56 20 11 31 |he volum|e .3V .1|
|00001ae0| 6f 66 20 74 68 65 0d 0a | 00 62 6f 78 20 61 73 20 |of the..|.box as |
|00001af0| 61 20 66 75 6e 63 74 69 | 6f 6e 20 6f 66 20 11 33 |a functi|on of .3|
|00001b00| 78 11 31 2e 20 20 57 68 | 61 74 20 69 73 20 74 68 |x.1. Wh|at is th|
|00001b10| 65 0d 0a 00 64 6f 6d 61 | 69 6e 20 6f 66 20 74 68 |e...doma|in of th|
|00001b20| 69 73 20 66 75 6e 63 74 | 69 6f 6e 3f 0d 0a 00 0d |is funct|ion?....|
|00001b30| 0b 00 13 12 31 53 4f 4c | 55 54 49 4f 4e 12 30 0d |....1SOL|UTION.0.|
|00001b40| 0a 00 54 68 65 20 76 6f | 6c 75 6d 65 20 6f 66 20 |..The vo|lume of |
|00001b50| 74 68 65 20 62 6f 78 20 | 69 73 20 67 69 76 65 6e |the box |is given|
|00001b60| 20 62 79 20 69 74 73 20 | 6c 65 6e 67 74 68 2c 20 | by its |length, |
|00001b70| 74 69 6d 65 73 20 69 74 | 73 20 77 69 64 74 68 2c |times it|s width,|
|00001b80| 20 74 69 6d 65 73 20 69 | 74 73 0d 0a 00 68 65 69 | times i|ts...hei|
|00001b90| 67 68 74 2e 20 20 54 68 | 65 72 65 66 6f 72 65 2c |ght. Th|erefore,|
|00001ba0| 20 77 65 20 68 61 76 65 | 0d 0a 00 0d 0b 00 20 20 | we have|...... |
|00001bb0| 20 20 20 20 20 20 20 20 | 20 20 56 6f 6c 75 6d 65 | | Volume|
|00001bc0| 20 3d 20 28 31 36 20 2d | 20 32 11 33 78 11 31 29 | = (16 -| 2.3x.1)|
|00001bd0| 28 31 36 20 2d 20 32 11 | 33 78 11 31 29 28 11 33 |(16 - 2.|3x.1)(.3|
|00001be0| 78 11 31 29 13 0d 0a 00 | 20 20 20 20 20 20 20 20 |x.1)....| |
|00001bf0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001c00| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 32 32 0d | | .22.|
|00001c10| 0b 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.. | |
|00001c20| 20 20 20 20 20 11 31 3d | 20 28 32 35 36 20 2d 20 | .1=| (256 - |
|00001c30| 36 34 11 33 78 20 11 31 | 2b 20 34 11 33 78 20 11 |64.3x .1|+ 4.3x .|
|00001c40| 31 29 28 11 33 78 11 31 | 29 13 0d 0a 00 20 20 20 |1)(.3x.1|).... |
|00001c50| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001c60| 20 20 20 20 11 32 33 20 | 20 20 20 20 20 32 0d 0b | .23 | 2..|
|00001c70| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
|00001c80| 20 20 20 20 11 31 3d 20 | 34 11 33 78 20 20 11 31 | .1= |4.3x .1|
|00001c90| 2d 20 36 34 11 33 78 20 | 20 11 31 2b 20 32 35 36 |- 64.3x | .1+ 256|
|00001ca0| 11 33 78 20 11 31 2e 13 | 0d 0a 00 0d 0b 00 55 73 |.3x .1..|......Us|
|00001cb0| 69 6e 67 20 66 75 6e 63 | 74 69 6f 6e 20 6e 6f 74 |ing func|tion not|
|00001cc0| 61 74 69 6f 6e 2c 20 77 | 65 20 68 61 76 65 0d 0a |ation, w|e have..|
|00001cd0| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
|00001ce0| 20 20 20 20 20 20 20 20 | 11 32 33 20 20 20 20 20 | |.23 |
|00001cf0| 20 32 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 | 2... | |
|00001d00| 20 20 20 11 33 56 11 31 | 28 11 33 78 11 31 29 20 | .3V.1|(.3x.1) |
|00001d10| 3d 20 34 11 33 78 20 20 | 11 31 2d 20 36 34 11 33 |= 4.3x |.1- 64.3|
|00001d20| 78 20 20 11 31 2b 20 32 | 35 36 11 33 78 20 11 31 |x .1+ 2|56.3x .1|
|00001d30| 2e 0d 0a 00 0d 0b 00 53 | 69 6e 63 65 20 74 68 65 |.......S|ince the|
|00001d40| 20 6f 62 6a 65 63 74 20 | 68 65 72 65 20 77 61 73 | object |here was|
|00001d50| 20 74 6f 20 63 72 65 61 | 74 65 20 61 20 62 6f 78 | to crea|te a box|
|00001d60| 2c 20 11 33 78 20 11 31 | 63 61 6e 6e 6f 74 20 65 |, .3x .1|cannot e|
|00001d70| 71 75 61 6c 20 7a 65 72 | 6f 2c 20 61 6e 64 20 6e |qual zer|o, and n|
|00001d80| 65 67 61 74 69 76 65 0d | 0a 00 76 61 6c 75 65 73 |egative.|..values|
|00001d90| 20 6f 66 20 11 33 78 20 | 11 31 73 69 6d 70 6c 79 | of .3x |.1simply|
|00001da0| 20 64 6f 6e 27 74 20 6d | 61 6b 65 20 73 65 6e 73 | don't m|ake sens|
|00001db0| 65 2e 13 0d 0a 00 0d 0b | 00 57 65 20 63 61 6e 20 |e.......|.We can |
|00001dc0| 61 6c 73 6f 20 6c 69 6d | 69 74 20 11 33 78 20 11 |also lim|it .3x .|
|00001dd0| 31 74 6f 20 76 61 6c 75 | 65 73 20 6c 65 73 73 20 |1to valu|es less |
|00001de0| 74 68 61 6e 20 38 2c 20 | 73 69 6e 63 65 20 74 68 |than 8, |since th|
|00001df0| 65 20 6f 72 69 67 69 6e | 61 6c 20 6d 61 74 65 72 |e origin|al mater|
|00001e00| 69 61 6c 20 69 73 20 6f | 6e 6c 79 0d 0a 00 31 36 |ial is o|nly...16|
|00001e10| 20 69 6e 63 68 65 73 20 | 77 69 64 65 2e 13 0d 0a | inches |wide....|
|00001e20| 00 0d 0b 00 54 68 65 72 | 65 66 6f 72 65 2c 20 74 |....Ther|efore, t|
|00001e30| 68 65 20 64 6f 6d 61 69 | 6e 20 6f 66 20 74 68 69 |he domai|n of thi|
|00001e40| 73 20 66 75 6e 63 74 69 | 6f 6e 20 69 73 20 61 6c |s functi|on is al|
|00001e50| 6c 20 72 65 61 6c 20 76 | 61 6c 75 65 73 20 6f 66 |l real v|alues of|
|00001e60| 20 11 33 78 20 11 31 73 | 75 63 68 20 74 68 61 74 | .3x .1s|uch that|
|00001e70| 0d 0a 00 0d 0b 00 20 20 | 20 20 20 20 20 20 20 20 |...... | |
|00001e80| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001e90| 20 30 20 3c 20 11 33 78 | 20 11 31 3c 20 38 20 2e | 0 < .3x| .1< 8 .|
|00001ea0| 0d 0a 00 53 65 63 74 69 | 6f 6e 20 32 2e 32 20 20 |...Secti|on 2.2 |
|00001eb0| 46 75 6e 63 74 69 6f 6e | 73 0d 0b 00 41 20 63 6f |Function|s...A co|
|00001ec0| 6d 70 61 6e 79 20 70 72 | 6f 64 75 63 65 73 20 61 |mpany pr|oduces a|
|00001ed0| 20 70 72 6f 64 75 63 74 | 20 66 6f 72 20 77 68 69 | product| for whi|
|00001ee0| 63 68 20 74 68 65 20 76 | 61 72 69 61 62 6c 65 20 |ch the v|ariable |
|00001ef0| 63 6f 73 74 20 69 73 20 | 24 31 30 2e 30 30 20 70 |cost is |$10.00 p|
|00001f00| 65 72 20 75 6e 69 74 0d | 0a 00 61 6e 64 20 74 68 |er unit.|..and th|
|00001f10| 65 20 66 69 78 65 64 20 | 63 6f 73 74 73 20 61 72 |e fixed |costs ar|
|00001f20| 65 20 24 31 32 35 2c 30 | 30 30 2e 20 20 54 68 65 |e $125,0|00. The|
|00001f30| 20 70 72 6f 64 75 63 74 | 20 73 65 6c 6c 73 20 66 | product| sells f|
|00001f40| 6f 72 20 24 31 35 2e 30 | 30 2e 20 20 4c 65 74 20 |or $15.0|0. Let |
|00001f50| 11 33 78 20 11 31 62 65 | 20 74 68 65 0d 0a 00 6e |.3x .1be| the...n|
|00001f60| 75 6d 62 65 72 20 6f 66 | 20 75 6e 69 74 73 20 70 |umber of| units p|
|00001f70| 72 6f 64 75 63 65 64 2e | 20 20 57 72 69 74 65 20 |roduced.| Write |
|00001f80| 74 68 65 20 74 6f 74 61 | 6c 20 63 6f 73 74 20 11 |the tota|l cost .|
|00001f90| 33 43 11 31 2c 20 74 68 | 65 20 74 6f 74 61 6c 20 |3C.1, th|e total |
|00001fa0| 72 65 76 65 6e 75 65 20 | 11 33 52 11 31 2c 20 61 |revenue |.3R.1, a|
|00001fb0| 6e 64 0d 0a 00 74 68 65 | 20 74 6f 74 61 6c 20 70 |nd...the| total p|
|00001fc0| 72 6f 66 69 74 20 11 33 | 50 11 31 2c 20 61 73 20 |rofit .3|P.1, as |
|00001fd0| 61 20 66 75 6e 63 74 69 | 6f 6e 20 6f 66 20 11 33 |a functi|on of .3|
|00001fe0| 78 11 31 2e 20 20 52 65 | 6d 65 6d 62 65 72 2c 20 |x.1. Re|member, |
|00001ff0| 11 33 50 20 11 31 3d 20 | 11 33 52 20 11 31 2d 20 |.3P .1= |.3R .1- |
|00002000| 11 33 43 11 31 2e 0d 0a | 00 0d 0b 00 13 12 31 53 |.3C.1...|......1S|
|00002010| 4f 4c 55 54 49 4f 4e 12 | 30 0d 0a 00 54 68 65 20 |OLUTION.|0...The |
|00002020| 74 6f 74 61 6c 20 63 6f | 73 74 20 69 73 20 67 69 |total co|st is gi|
|00002030| 76 65 6e 20 62 79 20 74 | 68 65 20 66 75 6e 63 74 |ven by t|he funct|
|00002040| 69 6f 6e 0d 0a 00 0d 0b | 00 20 20 20 20 20 20 20 |ion.....|. |
|00002050| 20 20 20 20 20 20 20 20 | 20 11 33 43 20 11 31 3d | | .3C .1=|
|00002060| 20 31 30 11 33 78 20 11 | 31 2b 20 31 32 35 2c 30 | 10.3x .|1+ 125,0|
|00002070| 30 30 20 2e 13 0d 0a 00 | 0d 0b 00 54 68 65 20 74 |00 .....|...The t|
|00002080| 6f 74 61 6c 20 72 65 76 | 65 6e 75 65 20 69 73 20 |otal rev|enue is |
|00002090| 67 69 76 65 6e 20 62 79 | 20 74 68 65 20 66 75 6e |given by| the fun|
|000020a0| 63 74 69 6f 6e 0d 0a 00 | 0d 0b 00 20 20 20 20 20 |ction...|... |
|000020b0| 20 20 20 20 20 20 20 20 | 20 20 20 11 33 52 20 11 | | .3R .|
|000020c0| 31 3d 20 31 35 11 33 78 | 20 11 31 2e 13 0d 0a 00 |1= 15.3x| .1.....|
|000020d0| 0d 0b 00 55 73 69 6e 67 | 20 74 68 65 73 65 20 74 |...Using| these t|
|000020e0| 77 6f 20 65 71 75 61 74 | 69 6f 6e 73 2c 20 77 65 |wo equat|ions, we|
|000020f0| 20 6f 62 74 61 69 6e 20 | 74 68 65 20 74 6f 74 61 | obtain |the tota|
|00002100| 6c 20 70 72 6f 66 69 74 | 20 66 75 6e 63 74 69 6f |l profit| functio|
|00002110| 6e 2e 0d 0a 00 0d 0b 00 | 20 20 20 20 20 20 20 20 |n.......| |
|00002120| 20 20 20 20 20 20 20 20 | 11 33 50 20 11 31 3d 20 | |.3P .1= |
|00002130| 31 35 11 33 78 20 11 31 | 2d 20 28 31 30 11 33 78 |15.3x .1|- (10.3x|
|00002140| 20 11 31 2b 20 31 32 35 | 2c 30 30 30 29 13 0d 0a | .1+ 125|,000)...|
|00002150| 00 0d 0b 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |.... | |
|00002160| 20 20 20 20 20 20 3d 20 | 35 11 33 78 20 11 31 2d | = |5.3x .1-|
|00002170| 20 31 32 35 2c 30 30 30 | 0d 0a 00 53 65 63 74 69 | 125,000|...Secti|
|00002180| 6f 6e 20 32 2e 32 20 20 | 46 75 6e 63 74 69 6f 6e |on 2.2 |Function|
|00002190| 73 0d 0b 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |s... | |
|000021a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000021b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000021c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000021d0| 33 0d 0b 00 46 69 6e 64 | 20 61 6c 6c 20 72 65 61 |3...Find| all rea|
|000021e0| 6c 20 76 61 6c 75 65 73 | 20 6f 66 20 11 33 78 20 |l values| of .3x |
|000021f0| 11 31 73 75 63 68 20 74 | 68 61 74 20 11 33 66 11 |.1such t|hat .3f.|
|00002200| 31 28 11 33 78 11 31 29 | 20 3d 20 30 20 77 68 65 |1(.3x.1)| = 0 whe|
|00002210| 72 65 20 11 33 66 11 31 | 28 11 33 78 11 31 29 20 |re .3f.1|(.3x.1) |
|00002220| 3d 20 11 34 32 32 32 32 | 32 20 11 31 2b 20 11 33 |= .42222|2 .1+ .3|
|00002230| 78 20 11 31 2e 0d 0b 00 | 20 20 20 20 20 20 20 20 |x .1....| |
|00002240| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002250| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002260| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002270| 20 20 11 33 78 20 11 31 | 2d 20 34 0d 0a 00 13 12 | .3x .1|- 4.....|
|00002280| 31 53 4f 4c 55 54 49 4f | 4e 12 30 0d 0a 00 0d 0b |1SOLUTIO|N.0.....|
|00002290| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
|000022a0| 20 20 11 33 66 11 31 28 | 11 33 78 11 31 29 20 3d | .3f.1(|.3x.1) =|
|000022b0| 20 30 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | 0 | |
|000022c0| 12 31 11 32 4c 65 74 20 | 66 28 78 29 20 65 71 75 |.1.2Let |f(x) equ|
|000022d0| 61 6c 20 30 11 31 12 30 | 13 0d 0a 00 0d 0b 00 20 |al 0.1.0|....... |
|000022e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 33 20 20 | | 3 |
|000022f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002300| 20 20 20 20 20 20 12 31 | 20 20 20 20 20 20 20 20 | .1| |
|00002310| 20 20 20 20 11 32 33 20 | 20 20 20 20 20 20 20 20 | .23 | |
|00002320| 20 20 20 20 20 11 31 12 | 30 0d 0b 00 20 20 20 20 | .1.|0... |
|00002330| 20 20 20 20 20 20 20 20 | 11 34 32 32 32 32 32 20 | |.422222 |
|00002340| 11 31 2b 20 11 33 78 20 | 11 31 3d 20 30 20 20 20 |.1+ .3x |.1= 0 |
|00002350| 20 20 20 20 20 20 20 20 | 20 20 20 12 31 11 32 53 | | .1.2S|
|00002360| 75 62 73 74 69 74 75 74 | 65 20 11 34 32 32 32 20 |ubstitut|e .4222 |
|00002370| 11 32 2b 20 78 20 66 6f | 72 20 66 28 78 29 11 31 |.2+ x fo|r f(x).1|
|00002380| 12 30 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 |.0... | |
|00002390| 20 11 33 78 20 11 31 2d | 20 34 20 20 20 20 20 20 | .3x .1-| 4 |
|000023a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000023b0| 12 31 20 20 20 20 20 20 | 20 20 20 20 20 11 32 78 |.1 | .2x|
|000023c0| 2d 34 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 |-4 | .|
|000023d0| 31 12 30 13 0d 0a 00 0d | 0b 00 20 20 20 20 20 20 |1.0.....|.. |
|000023e0| 33 20 20 20 20 20 20 11 | 33 78 11 31 28 11 33 78 |3 .|3x.1(.3x|
|000023f0| 20 11 31 2d 20 34 29 0d | 0b 00 20 20 20 20 11 34 | .1- 4).|.. .4|
|00002400| 32 32 32 32 32 20 11 31 | 2b 20 11 34 32 32 32 32 |22222 .1|+ .42222|
|00002410| 32 32 32 32 32 20 11 31 | 3d 20 30 20 20 20 20 20 |22222 .1|= 0 |
|00002420| 20 20 20 20 20 20 20 20 | 20 12 31 11 32 46 69 6e | | .1.2Fin|
|00002430| 64 20 6c 65 61 73 74 20 | 63 6f 6d 6d 6f 6e 20 64 |d least |common d|
|00002440| 65 6e 6f 6d 69 6e 61 74 | 6f 72 11 31 12 30 0d 0b |enominat|or.1.0..|
|00002450| 00 20 20 20 20 11 33 78 | 20 11 31 2d 20 34 20 20 |. .3x| .1- 4 |
|00002460| 20 20 20 11 33 78 20 11 | 31 2d 20 34 20 20 20 20 | .3x .|1- 4 |
|00002470| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002480| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002490| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000024a0| 20 20 20 13 0d 0a 00 20 | 20 20 20 20 20 20 20 20 | .... | |
|000024b0| 20 20 20 20 20 20 11 32 | 32 0d 0b 00 20 20 20 20 | .2|2... |
|000024c0| 20 20 20 20 20 20 11 31 | 33 20 2b 20 11 33 78 20 | .1|3 + .3x |
|000024d0| 20 11 31 2d 20 34 11 33 | 78 0d 0b 00 20 20 20 20 | .1- 4.3|x... |
|000024e0| 20 20 20 20 20 20 11 34 | 32 32 32 32 32 32 32 32 | .4|22222222|
|000024f0| 32 32 32 20 11 31 3d 20 | 30 20 20 20 20 20 20 20 |222 .1= |0 |
|00002500| 20 20 20 20 20 20 20 12 | 31 11 32 43 6f 6d 62 69 | .|1.2Combi|
|00002510| 6e 65 20 65 78 70 72 65 | 73 73 69 6f 6e 73 11 31 |ne expre|ssions.1|
|00002520| 12 30 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 |.0... | |
|00002530| 20 20 11 33 78 20 11 31 | 2d 20 34 20 20 20 20 20 | .3x .1|- 4 |
|00002540| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002550| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002560| 20 20 20 20 20 20 20 20 | 20 13 0d 0a 00 20 20 20 | | .... |
|00002570| 20 20 20 20 20 20 20 20 | 11 32 32 0d 0b 00 20 20 | |.22... |
|00002580| 20 20 20 20 20 20 20 20 | 11 33 78 20 20 11 31 2d | |.3x .1-|
|00002590| 20 34 11 33 78 20 11 31 | 2b 20 33 20 3d 20 30 20 | 4.3x .1|+ 3 = 0 |
|000025a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 12 31 11 | | .1.|
|000025b0| 32 4d 75 6c 74 69 70 6c | 79 20 62 6f 74 68 20 73 |2Multipl|y both s|
|000025c0| 69 64 65 73 20 62 79 20 | 78 2d 34 11 31 12 30 13 |ides by |x-4.1.0.|
|000025d0| 0d 0a 00 0d 0a 00 20 20 | 20 20 20 20 20 28 11 33 |...... | (.3|
|000025e0| 78 20 11 31 2d 20 33 29 | 28 11 33 78 20 11 31 2d |x .1- 3)|(.3x .1-|
|000025f0| 20 31 29 20 3d 20 30 20 | 20 20 20 20 20 20 20 20 | 1) = 0 | |
|00002600| 20 20 20 20 20 12 31 11 | 32 46 61 63 74 6f 72 11 | .1.|2Factor.|
|00002610| 31 12 30 13 0d 0a 00 0d | 0b 00 46 72 6f 6d 20 6f |1.0.....|..From o|
|00002620| 75 72 20 66 69 6e 61 6c | 20 65 71 75 61 74 69 6f |ur final| equatio|
|00002630| 6e 2c 20 77 65 20 73 65 | 65 20 74 68 61 74 20 11 |n, we se|e that .|
|00002640| 33 66 11 31 28 11 33 78 | 11 31 29 20 3d 20 30 20 |3f.1(.3x|.1) = 0 |
|00002650| 77 68 65 6e 20 11 33 78 | 20 11 31 3d 20 33 20 61 |when .3x| .1= 3 a|
|00002660| 6e 64 20 77 68 65 6e 20 | 11 33 78 20 11 31 3d 20 |nd when |.3x .1= |
|00002670| 31 2e 0d 0a 00 53 65 63 | 74 69 6f 6e 20 32 2e 32 |1....Sec|tion 2.2|
|00002680| 20 20 46 75 6e 63 74 69 | 6f 6e 73 0d 0b 00 41 73 | Functi|ons...As|
|00002690| 73 75 6d 65 20 74 68 61 | 74 20 74 68 65 20 64 6f |sume tha|t the do|
|000026a0| 6d 61 69 6e 20 6f 66 20 | 11 33 66 20 11 31 69 73 |main of |.3f .1is|
|000026b0| 20 74 68 65 20 73 65 74 | 20 11 33 41 20 11 31 3d | the set| .3A .1=|
|000026c0| 20 7b 2d 32 2c 20 2d 31 | 2c 20 30 2c 20 31 2c 20 | {-2, -1|, 0, 1, |
|000026d0| 32 7d 2e 20 20 44 65 74 | 65 72 6d 69 6e 65 20 74 |2}. Det|ermine t|
|000026e0| 68 65 0d 0a 00 73 65 74 | 20 6f 66 20 6f 72 64 65 |he...set| of orde|
|000026f0| 72 65 64 20 70 61 69 72 | 73 20 74 68 61 74 20 72 |red pair|s that r|
|00002700| 65 70 72 65 73 65 6e 74 | 73 20 74 68 65 20 66 75 |epresent|s the fu|
|00002710| 6e 63 74 69 6f 6e 20 11 | 33 66 11 31 2c 20 69 66 |nction .|3f.1, if|
|00002720| 20 11 33 66 11 31 28 11 | 33 78 11 31 29 20 3d 20 | .3f.1(.|3x.1) = |
|00002730| 32 11 33 78 20 11 31 2d | 20 33 2e 0d 0a 00 0d 0b |2.3x .1-| 3......|
|00002740| 00 13 12 31 53 4f 4c 55 | 54 49 4f 4e 12 30 0d 0a |...1SOLU|TION.0..|
|00002750| 00 57 65 20 62 65 67 69 | 6e 20 62 79 20 63 61 6c |.We begi|n by cal|
|00002760| 63 75 6c 61 74 69 6e 67 | 20 74 68 65 20 6f 72 64 |culating| the ord|
|00002770| 65 72 65 64 20 70 61 69 | 72 20 63 6f 72 72 65 73 |ered pai|r corres|
|00002780| 70 6f 6e 64 69 6e 67 20 | 74 6f 20 65 61 63 68 20 |ponding |to each |
|00002790| 76 61 6c 75 65 20 69 6e | 20 74 68 65 0d 0a 00 64 |value in| the...d|
|000027a0| 6f 6d 61 69 6e 2e 13 0d | 0a 00 0d 0b 00 20 20 20 |omain...|..... |
|000027b0| 20 20 20 20 20 11 33 66 | 11 31 28 2d 32 29 20 3d | .3f|.1(-2) =|
|000027c0| 20 32 28 2d 32 29 20 2d | 20 33 20 3d 20 2d 37 20 | 2(-2) -| 3 = -7 |
|000027d0| 20 20 20 20 20 11 34 35 | 35 35 36 20 20 20 20 20 | .45|556 |
|000027e0| 20 11 31 28 2d 32 2c 20 | 2d 37 29 13 0d 0a 00 0d | .1(-2, |-7).....|
|000027f0| 0b 00 20 20 20 20 20 20 | 20 20 11 33 66 11 31 28 |.. | .3f.1(|
|00002800| 2d 31 29 20 3d 20 32 28 | 2d 31 29 20 2d 20 33 20 |-1) = 2(|-1) - 3 |
|00002810| 3d 20 2d 35 20 20 20 20 | 20 20 11 34 35 35 35 36 |= -5 | .45556|
|00002820| 20 20 20 20 20 20 11 31 | 28 2d 31 2c 20 2d 35 29 | .1|(-1, -5)|
|00002830| 13 0d 0a 00 0d 0b 00 20 | 20 20 20 20 20 20 20 20 |....... | |
|00002840| 11 33 66 11 31 28 30 29 | 20 3d 20 32 28 30 29 20 |.3f.1(0)| = 2(0) |
|00002850| 2d 20 33 20 3d 20 2d 33 | 20 20 20 20 20 20 20 11 |- 3 = -3| .|
|00002860| 34 35 35 35 36 20 20 20 | 20 20 20 11 31 28 30 2c |45556 | .1(0,|
|00002870| 20 2d 33 29 13 0d 0a 00 | 0d 0b 00 20 20 20 20 20 | -3)....|... |
|00002880| 20 20 20 20 11 33 66 11 | 31 28 31 29 20 3d 20 32 | .3f.|1(1) = 2|
|00002890| 28 31 29 20 2d 20 33 20 | 3d 20 2d 31 20 20 20 20 |(1) - 3 |= -1 |
|000028a0| 20 20 20 11 34 35 35 35 | 36 20 20 20 20 20 20 11 | .4555|6 .|
|000028b0| 31 28 31 2c 20 2d 31 29 | 13 0d 0a 00 0d 0b 00 20 |1(1, -1)|....... |
|000028c0| 20 20 20 20 20 20 20 20 | 11 33 66 11 31 28 32 29 | |.3f.1(2)|
|000028d0| 20 3d 20 32 28 32 29 20 | 2d 20 33 20 3d 20 31 20 | = 2(2) |- 3 = 1 |
|000028e0| 20 20 20 20 20 20 20 11 | 34 35 35 35 36 20 20 20 | .|45556 |
|000028f0| 20 20 20 11 31 28 32 2c | 20 31 29 13 0d 0a 00 0d | .1(2,| 1).....|
|00002900| 0b 00 54 68 75 73 2c 20 | 74 68 65 20 6f 72 64 65 |..Thus, |the orde|
|00002910| 72 65 64 20 70 61 69 72 | 73 20 61 72 65 20 7b 28 |red pair|s are {(|
|00002920| 2d 32 2c 20 2d 37 29 2c | 20 28 2d 31 2c 20 2d 35 |-2, -7),| (-1, -5|
|00002930| 29 2c 20 28 30 2c 20 2d | 33 29 2c 20 28 31 2c 20 |), (0, -|3), (1, |
|00002940| 2d 31 29 2c 20 28 32 2c | 20 31 29 7d 2e 0d 0a 00 |-1), (2,| 1)}....|
|00002950| 53 65 63 74 69 6f 6e 20 | 32 2e 32 20 20 46 75 6e |Section |2.2 Fun|
|00002960| 63 74 69 6f 6e 73 0d 0b | 00 46 69 6e 64 20 74 68 |ctions..|.Find th|
|00002970| 65 20 76 61 6c 75 65 73 | 20 6f 66 20 11 33 78 20 |e values| of .3x |
|00002980| 11 31 66 6f 72 20 77 68 | 69 63 68 20 11 33 66 11 |.1for wh|ich .3f.|
|00002990| 31 28 11 33 78 11 31 29 | 20 3d 20 11 33 67 11 31 |1(.3x.1)| = .3g.1|
|000029a0| 28 11 33 78 11 31 29 20 | 66 6f 72 0d 0a 00 20 20 |(.3x.1) |for... |
|000029b0| 20 20 20 20 20 20 20 20 | 20 20 20 11 32 33 0d 0b | | .23..|
|000029c0| 00 20 20 20 20 20 11 33 | 66 11 31 28 11 33 78 11 |. .3|f.1(.3x.|
|000029d0| 31 29 20 3d 20 11 33 78 | 20 20 11 31 2d 20 32 11 |1) = .3x| .1- 2.|
|000029e0| 33 78 20 20 20 11 31 61 | 6e 64 20 20 20 11 33 67 |3x .1a|nd .3g|
|000029f0| 11 31 28 11 33 78 11 31 | 29 20 3d 20 2d 11 33 78 |.1(.3x.1|) = -.3x|
|00002a00| 11 31 2e 0d 0a 00 0d 0b | 00 13 12 31 53 4f 4c 55 |.1......|...1SOLU|
|00002a10| 54 49 4f 4e 12 30 0d 0a | 00 0d 0b 00 54 6f 20 73 |TION.0..|....To s|
|00002a20| 6f 6c 76 65 20 74 68 69 | 73 20 70 72 6f 62 6c 65 |olve thi|s proble|
|00002a30| 6d 2c 20 77 65 20 6c 65 | 74 20 11 33 66 11 31 28 |m, we le|t .3f.1(|
|00002a40| 11 33 78 11 31 29 20 3d | 20 11 33 67 11 31 28 11 |.3x.1) =| .3g.1(.|
|00002a50| 33 78 11 31 29 20 61 6e | 64 20 73 6f 6c 76 65 20 |3x.1) an|d solve |
|00002a60| 66 6f 72 20 11 33 78 11 | 31 2c 20 61 73 20 66 6f |for .3x.|1, as fo|
|00002a70| 6c 6c 6f 77 73 2e 0d 0a | 00 0d 0b 00 20 20 20 20 |llows...|.... |
|00002a80| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 33 66 11 | | .3f.|
|00002a90| 31 28 11 33 78 11 31 29 | 20 3d 20 11 33 67 11 31 |1(.3x.1)| = .3g.1|
|00002aa0| 28 11 33 78 11 31 29 20 | 20 20 20 20 20 20 20 20 |(.3x.1) | |
|00002ab0| 20 11 32 12 31 4c 65 74 | 20 66 28 78 29 20 65 71 | .2.1Let| f(x) eq|
|00002ac0| 75 61 6c 20 67 28 78 29 | 12 30 11 31 13 0d 0a 00 |ual g(x)|.0.1....|
|00002ad0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 32 | | .2|
|00002ae0| 33 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |3 | |
|00002af0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002b00| 20 20 20 20 20 20 20 20 | 20 20 12 31 33 12 30 0d | | .13.0.|
|00002b10| 0b 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 |.. | .|
|00002b20| 33 78 20 20 11 31 2d 20 | 32 11 33 78 20 11 31 3d |3x .1- |2.3x .1=|
|00002b30| 20 2d 11 33 78 20 20 20 | 20 20 20 20 20 20 20 20 | -.3x | |
|00002b40| 20 11 32 12 31 53 75 62 | 73 74 69 74 75 74 65 20 | .2.1Sub|stitute |
|00002b50| 66 28 78 29 20 3d 20 78 | 20 20 2d 20 32 78 20 61 |f(x) = x| - 2x a|
|00002b60| 6e 64 20 67 28 78 29 20 | 3d 20 2d 78 12 30 11 31 |nd g(x) |= -x.0.1|
|00002b70| 13 0d 0a 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |.... | |
|00002b80| 20 20 20 11 32 33 0d 0b | 00 20 20 20 20 20 20 20 | .23..|. |
|00002b90| 20 20 20 20 20 20 20 11 | 33 78 20 20 11 31 2d 20 | .|3x .1- |
|00002ba0| 11 33 78 20 11 31 3d 20 | 30 20 20 20 20 20 20 20 |.3x .1= |0 |
|00002bb0| 20 20 20 20 20 20 11 32 | 12 31 41 64 64 20 78 20 | .2|.1Add x |
|00002bc0| 74 6f 20 62 6f 74 68 20 | 73 69 64 65 73 12 30 11 |to both |sides.0.|
|00002bd0| 31 13 0d 0a 00 20 20 20 | 20 20 20 20 20 20 20 20 |1.... | |
|00002be0| 20 20 20 11 32 32 0d 0b | 00 20 20 20 20 20 20 20 | .22..|. |
|00002bf0| 20 20 20 20 11 33 78 11 | 31 28 78 20 20 2d 20 31 | .3x.|1(x - 1|
|00002c00| 29 20 3d 20 30 20 20 20 | 20 20 20 20 20 20 20 20 |) = 0 | |
|00002c10| 20 20 11 32 12 31 46 61 | 63 74 6f 72 20 6f 75 74 | .2.1Fa|ctor out|
|00002c20| 20 63 6f 6d 6d 6f 6e 20 | 6d 6f 6e 6f 6d 69 61 6c | common |monomial|
|00002c30| 12 30 11 31 13 0d 0a 00 | 0d 0b 00 20 20 20 20 20 |.0.1....|... |
|00002c40| 11 33 78 11 31 28 11 33 | 78 20 11 31 2d 20 31 29 |.3x.1(.3|x .1- 1)|
|00002c50| 28 11 33 78 20 11 31 2b | 20 31 29 20 3d 20 30 20 |(.3x .1+| 1) = 0 |
|00002c60| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 32 12 31 | | .2.1|
|00002c70| 46 61 63 74 6f 72 20 64 | 69 66 66 65 72 65 6e 63 |Factor d|ifferenc|
|00002c80| 65 20 6f 66 20 73 71 75 | 61 72 65 73 12 30 11 31 |e of squ|ares.0.1|
|00002c90| 13 0d 0a 00 0d 0b 00 20 | 20 20 20 20 20 20 20 20 |....... | |
|00002ca0| 20 20 20 20 20 20 20 20 | 20 20 11 33 78 20 11 31 | | .3x .1|
|00002cb0| 3d 20 30 2c 20 2d 31 2c | 20 31 20 20 20 20 20 20 |= 0, -1,| 1 |
|00002cc0| 11 32 12 31 53 6f 6c 76 | 65 20 66 6f 72 20 78 12 |.2.1Solv|e for x.|
|00002cd0| 30 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |0 | |
|00002ce0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002cf0| 20 20 20 20 20 20 20 20 | 11 31 2e 0d 0a 00 26 00 | |.1....&.|
|00002d00| 00 00 af 02 00 00 4d 16 | 00 00 10 00 00 00 00 00 |......M.|........|
|00002d10| 00 00 65 32 2d 32 00 eb | 02 00 00 76 07 00 00 4d |..e2-2..|...v...M|
|00002d20| 16 00 00 d5 02 00 00 00 | 00 00 00 65 32 2d 32 2d |........|...e2-2-|
|00002d30| 31 00 77 0a 00 00 1f 04 | 00 00 4d 16 00 00 61 0a |1.w.....|..M...a.|
|00002d40| 00 00 00 00 00 00 65 32 | 2d 32 2d 32 00 ac 0e 00 |......e2|-2-2....|
|00002d50| 00 fd 01 00 00 4d 16 00 | 00 96 0e 00 00 00 00 00 |.....M..|........|
|00002d60| 00 65 32 2d 32 2d 33 00 | bf 10 00 00 19 04 00 00 |.e2-2-3.|........|
|00002d70| 4d 16 00 00 a9 10 00 00 | 00 00 00 00 65 32 2d 32 |M.......|....e2-2|
|00002d80| 2d 34 00 ee 14 00 00 dc | 04 00 00 4d 16 00 00 d8 |-4......|...M....|
|00002d90| 14 00 00 00 00 00 00 65 | 32 2d 32 2d 35 00 e0 19 |.......e|2-2-5...|
|00002da0| 00 00 c3 04 00 00 4d 16 | 00 00 ca 19 00 00 00 00 |......M.|........|
|00002db0| 00 00 65 32 2d 32 2d 36 | 00 b9 1e 00 00 c2 02 00 |..e2-2-6|........|
|00002dc0| 00 4d 16 00 00 a3 1e 00 | 00 00 00 00 00 65 32 2d |.M......|.....e2-|
|00002dd0| 32 2d 37 00 91 21 00 00 | e4 04 00 00 4d 16 00 00 |2-7..!..|....M...|
|00002de0| 7b 21 00 00 00 00 00 00 | 69 32 2d 32 2d 31 00 8b |{!......|i2-2-1..|
|00002df0| 26 00 00 c5 02 00 00 4d | 16 00 00 75 26 00 00 00 |&......M|...u&...|
|00002e00| 00 00 00 69 32 2d 32 2d | 32 00 66 29 00 00 98 03 |...i2-2-|2.f)....|
|00002e10| 00 00 4d 16 00 00 50 29 | 00 00 00 00 00 00 69 32 |..M...P)|......i2|
|00002e20| 2d 32 2d 33 00 | |-2-3. | |
+--------+-------------------------+-------------------------+--------+--------+
