/ NeXT Education Software Sampler 1992 Fall / NeXT Education Software Sampler 1992 Fall.iso / Mathematics / Notebooks / CSOMinesCalculus / Chapter1 / ws2.tex

< prev

next >

MacOS 8.1

Win98

DOS

browse contents

view JSON data

view as text

+--------+-------------------------+-------------------------+--------+--------+
|00000000| 5c 64 6f 63 75 6d 65 6e | 74 73 74 79 6c 65 5b 66 |\documen|tstyle[f|
|00000010| 6c 65 71 6e 2c 65 70 73 | 66 2c 63 61 6c 63 5d 7b |leqn,eps|f,calc]{|
|00000020| 61 72 74 69 63 6c 65 7d | 0a 5c 6d 61 72 6b 72 69 |article}|.\markri|
|00000030| 67 68 74 7b 43 68 61 70 | 74 65 72 20 31 3a 20 57 |ght{Chap|ter 1: W|
|00000040| 6f 72 6b 73 68 65 65 74 | 20 32 7d 0a 5c 62 65 67 |orksheet| 2}.\beg|
|00000050| 69 6e 7b 64 6f 63 75 6d | 65 6e 74 7d 0a 0a 5c 42 |in{docum|ent}..\B|
|00000060| 66 7b 5c 53 74 61 72 5c | 20 5c 53 74 61 72 5c 20 |f{\Star\| \Star\ |
|00000070| 43 68 61 70 74 65 72 20 | 31 3a 20 57 6f 72 6b 73 |Chapter |1: Works|
|00000080| 68 65 65 74 20 32 20 20 | 5c 68 66 69 6c 6c 20 4a |heet 2  |\hfill J|
|00000090| 61 63 6b 20 4b 2e 20 43 | 6f 68 65 6e 20 5c 68 66 |ack K. C|ohen \hf|
|000000a0| 69 6c 6c 20 43 6f 6c 6f | 72 61 64 6f 20 53 63 68 |ill Colo|rado Sch|
|000000b0| 6f 6f 6c 20 6f 66 20 4d | 69 6e 65 73 7d 0a 0a 5c |ool of M|ines}..\|
|000000c0| 76 73 70 61 63 65 7b 31 | 2e 35 65 78 7d 0a 5c 43 |vspace{1|.5ex}.\C|
|000000d0| 62 7b 46 75 6e 63 74 69 | 6f 6e 73 2c 20 53 79 6d |b{Functi|ons, Sym|
|000000e0| 62 6f 6c 20 50 72 6f 62 | 6c 65 6d 73 7d 0a 5c 76 |bol Prob|lems}.\v|
|000000f0| 73 70 61 63 65 7b 31 2e | 35 65 78 7d 0a 0a 5c 6e |space{1.|5ex}..\n|
|00000100| 6f 69 6e 64 65 6e 74 20 | 5c 42 66 7b 53 75 67 67 |oindent |\Bf{Sugg|
|00000110| 65 73 74 65 64 20 50 72 | 6f 62 6c 65 6d 73 7d 0a |ested Pr|oblems}.|
|00000120| 53 65 63 74 69 6f 6e 20 | 31 2e 31 3a 20 32 37 2c |Section |1.1: 27,|
|00000130| 20 34 35 2c 20 35 35 0a | 0a 5c 62 65 67 69 6e 7b | 45, 55.|.\begin{|
|00000140| 65 6e 75 6d 65 72 61 74 | 65 7d 0a 5c 69 74 65 6d |enumerat|e}.\item|
|00000150| 20 49 74 20 69 73 20 69 | 6d 70 6f 72 74 61 6e 74 | It is i|mportant|
|00000160| 20 74 6f 20 75 6e 64 65 | 72 73 74 61 6e 64 20 74 | to unde|rstand t|
|00000170| 68 65 20 64 69 66 66 65 | 72 65 6e 63 65 20 62 65 |he diffe|rence be|
|00000180| 74 77 65 65 6e 20 61 20 | 5c 45 6d 7b 66 6f 72 6d |tween a |\Em{form|
|00000190| 75 6c 61 7d 20 61 6e 64 | 20 61 20 5c 45 6d 20 7b |ula} and| a \Em {|
|000001a0| 66 75 6e 63 74 69 6f 6e | 7d 2e 20 20 53 6f 6d 65 |function|}.  Some|
|000001b0| 20 66 75 6e 63 74 69 6f | 6e 73 20 61 72 65 20 73 | functio|ns are s|
|000001c0| 70 65 63 69 66 69 65 64 | 20 62 79 20 66 6f 72 6d |pecified| by form|
|000001d0| 75 6c 61 73 2d 2d 2d 62 | 75 74 20 74 68 65 72 65 |ulas---b|ut there|
|000001e0| 20 61 72 65 20 61 6c 73 | 6f 20 6f 74 68 65 72 20 | are als|o other |
|000001f0| 77 61 79 73 20 74 6f 20 | 73 70 65 63 69 66 79 20 |ways to |specify |
|00000200| 61 20 66 75 6e 63 74 69 | 6f 6e 2e 20 20 41 6e 64 |a functi|on.  And|
|00000210| 20 73 6f 6d 65 20 66 6f | 72 6d 75 6c 61 73 20 64 | some fo|rmulas d|
|00000220| 6f 20 5c 45 6d 7b 6e 6f | 74 7d 20 73 70 65 63 69 |o \Em{no|t} speci|
|00000230| 66 79 20 66 75 6e 63 74 | 69 6f 6e 73 2e 0a 0a 5c |fy funct|ions...\|
|00000240| 6e 6f 69 6e 64 65 6e 74 | 20 53 6f 6d 65 20 66 6f |noindent| Some fo|
|00000250| 72 6d 75 6c 61 73 20 66 | 6f 6c 6c 6f 77 2e 20 20 |rmulas f|ollow.  |
|00000260| 57 68 69 63 68 20 73 70 | 65 63 69 66 79 20 61 20 |Which sp|ecify a |
|00000270| 66 75 6e 63 74 69 6f 6e | 3f 20 46 6f 72 20 74 68 |function|? For th|
|00000280| 6f 73 65 20 74 68 61 74 | 20 64 6f 20 73 70 65 63 |ose that| do spec|
|00000290| 69 66 79 20 61 20 66 75 | 6e 63 74 69 6f 6e 2c 20 |ify a fu|nction, |
|000002a0| 77 68 61 74 20 69 73 20 | 74 68 65 20 60 60 6e 61 |what is |the ``na|
|000002b0| 74 75 72 61 6c 27 27 20 | 64 6f 6d 61 69 6e 20 61 |tural'' |domain a|
|000002c0| 6e 64 20 72 61 6e 67 65 | 20 28 73 65 65 20 70 61 |nd range| (see pa|
|000002d0| 67 65 20 36 20 6a 75 73 | 74 20 62 65 6c 6f 77 20 |ge 6 jus|t below |
|000002e0| 74 68 65 20 72 65 64 20 | 6c 69 6e 65 29 3f 20 20 |the red |line)?  |
|000002f0| 4f 6e 20 73 6f 6d 65 20 | 70 72 6f 62 6c 65 6d 73 |On some |problems|
|00000300| 2c 20 61 20 67 72 61 70 | 68 20 6d 69 67 68 74 20 |, a grap|h might |
|00000310| 68 65 6c 70 2e 20 20 59 | 6f 75 20 63 61 6e 20 67 |help.  Y|ou can g|
|00000320| 65 74 20 6f 6e 65 20 70 | 61 69 6e 6c 65 73 73 6c |et one p|ainlessl|
|00000330| 79 20 77 69 74 68 20 5c | 4d 6d 61 5c 20 61 73 20 |y with \|Mma\ as |
|00000340| 66 6f 6c 6c 6f 77 73 3a | 0a 0a 5c 6e 6f 69 6e 64 |follows:|..\noind|
|00000350| 65 6e 74 20 5c 54 74 7b | 50 6c 6f 74 5b 78 20 2b |ent \Tt{|Plot[x +|
|00000360| 20 35 2c 20 5c 7b 78 2c | 20 2d 35 2c 20 35 5c 7d | 5, \{x,| -5, 5\}|
|00000370| 5d 7d 0a 0a 5c 6e 6f 69 | 6e 64 65 6e 74 20 5c 54 |]}..\noi|ndent \T|
|00000380| 74 7b 50 6c 6f 74 5b 53 | 69 6e 5b 78 5d 20 2b 20 |t{Plot[S|in[x] + |
|00000390| 43 6f 73 5b 78 5d 2c 20 | 5c 7b 78 2c 20 2d 32 50 |Cos[x], |\{x, -2P|
|000003a0| 69 2c 20 32 50 69 5c 7d | 5d 7d 0a 0a 5c 6e 6f 69 |i, 2Pi\}|]}..\noi|
|000003b0| 6e 64 65 6e 74 20 61 6e | 64 20 73 6f 20 66 6f 72 |ndent an|d so for|
|000003c0| 74 68 2e 0a 0a 20 20 20 | 20 20 20 20 20 5c 62 65 |th...   |     \be|
|000003d0| 67 69 6e 7b 65 6e 75 6d | 65 72 61 74 65 7d 0a 20 |gin{enum|erate}. |
|000003e0| 20 20 20 20 20 20 20 5c | 69 74 65 6d 20 20 20 24 |       \|item   $|
|000003f0| 79 20 3d 20 78 20 2b 20 | 35 24 0a 20 20 20 20 20 |y = x + |5$.     |
|00000400| 20 20 20 5c 69 74 65 6d | 20 20 20 24 79 20 3d 20 |   \item|   $y = |
|00000410| 5c 73 69 6e 20 78 20 2b | 20 5c 63 6f 73 20 78 24 |\sin x +| \cos x$|
|00000420| 0a 20 20 20 20 20 20 20 | 20 5c 69 74 65 6d 20 20 |.       | \item  |
|00000430| 20 24 79 20 3d 20 31 20 | 2f 20 78 24 0a 20 20 20 | $y = 1 |/ x$.   |
|00000440| 20 20 20 20 20 5c 69 74 | 65 6d 20 20 20 24 79 20 |     \it|em   $y |
|00000450| 2d 20 78 20 2d 20 35 20 | 3d 20 30 24 0a 20 20 20 |- x - 5 |= 0$.   |
|00000460| 20 20 20 20 20 5c 69 74 | 65 6d 20 20 20 24 78 5e |     \it|em   $x^|
|00000470| 32 20 2b 20 79 5e 32 20 | 2d 20 34 20 3d 20 30 24 |2 + y^2 |- 4 = 0$|
|00000480| 0a 20 20 20 20 20 20 20 | 20 5c 69 74 65 6d 20 20 |.       | \item  |
|00000490| 20 24 78 5e 32 20 2b 20 | 79 5e 32 20 2b 20 34 20 | $x^2 + |y^2 + 4 |
|000004a0| 3d 20 30 24 0a 20 20 20 | 20 20 20 20 20 5c 65 6e |= 0$.   |     \en|
|000004b0| 64 7b 65 6e 75 6d 65 72 | 61 74 65 7d 0a 0a 5c 69 |d{enumer|ate}..\i|
|000004c0| 74 65 6d 20 46 75 6e 63 | 74 69 6f 6e 73 20 63 61 |tem Func|tions ca|
|000004d0| 6e 20 73 6f 6d 65 74 69 | 6d 65 73 20 62 65 20 73 |n someti|mes be s|
|000004e0| 70 65 63 69 66 69 65 64 | 20 62 79 20 74 61 62 6c |pecified| by tabl|
|000004f0| 65 73 2e 0a 20 20 20 20 | 20 20 20 20 5c 62 65 67 |es..    |    \beg|
|00000500| 69 6e 7b 65 6e 75 6d 65 | 72 61 74 65 7d 0a 20 20 |in{enume|rate}.  |
|00000510| 20 20 20 20 20 20 5c 69 | 74 65 6d 20 54 68 65 20 |      \i|tem The |
|00000520| 60 60 44 65 6e 76 65 72 | 20 44 69 61 72 79 27 27 |``Denver| Diary''|
|00000530| 20 66 6f 72 20 4a 75 6c | 79 20 31 35 2c 20 31 39 | for Jul|y 15, 19|
|00000540| 39 31 20 77 61 73 3a 0a | 20 20 20 20 20 20 20 20 |91 was:.|        |
|00000550| 0a 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.       |        |
|00000560| 20 5c 62 65 67 69 6e 7b | 74 61 62 75 6c 61 72 7d | \begin{|tabular}|
|00000570| 7b 6c 6c 7c 6c 6c 7d 20 | 20 5c 68 6c 69 6e 65 0a |{ll|ll} | \hline.|
|00000580| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00000590| 7b 5c 62 66 20 54 69 6d | 65 7d 20 26 20 7b 5c 62 |{\bf Tim|e} & {\b|
|000005a0| 66 20 54 65 6d 70 7d 20 | 26 20 7b 5c 62 66 20 54 |f Temp} |& {\bf T|
|000005b0| 69 6d 65 7d 20 26 20 7b | 5c 62 66 20 54 65 6d 70 |ime} & {|\bf Temp|
|000005c0| 7d 20 5c 5c 0a 20 20 20 | 20 20 20 20 20 20 20 20 |} \\.   |        |
|000005d0| 20 20 20 20 20 4d 64 6e | 74 20 26 20 37 32 20 26 |     Mdn|t & 72 &|
|000005e0| 20 4e 6f 6f 6e 20 26 20 | 38 37 20 5c 5c 0a 20 20 | Noon & |87 \\.  |
|000005f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 31 20 |        |      1 |
|00000600| 61 6d 20 26 20 36 39 20 | 26 20 31 20 70 6d 20 26 |am & 69 |& 1 pm &|
|00000610| 20 39 32 20 5c 5c 0a 20 | 20 20 20 20 20 20 20 20 | 92 \\. |        |
|00000620| 20 20 20 20 20 20 20 32 | 20 61 6d 20 26 20 36 37 |       2| am & 67|
|00000630| 20 26 20 32 20 70 6d 20 | 26 20 39 33 20 5c 5c 0a | & 2 pm |& 93 \\.|
|00000640| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00000650| 33 20 61 6d 20 26 20 36 | 33 20 26 20 33 20 70 6d |3 am & 6|3 & 3 pm|
|00000660| 20 26 20 39 35 20 5c 5c | 0a 20 20 20 20 20 20 20 | & 95 \\|.       |
|00000670| 20 20 20 20 20 20 20 20 | 20 34 20 61 6d 20 26 20 |        | 4 am & |
|00000680| 36 31 20 26 20 34 20 70 | 6d 20 26 20 39 36 20 5c |61 & 4 p|m & 96 \|
|00000690| 5c 0a 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |\.      |        |
|000006a0| 20 20 35 20 61 6d 20 26 | 20 35 38 20 26 20 35 20 |  5 am &| 58 & 5 |
|000006b0| 70 6d 20 26 20 39 37 20 | 5c 5c 0a 20 20 20 20 20 |pm & 97 |\\.     |
|000006c0| 20 20 20 20 20 20 20 20 | 20 20 20 36 20 61 6d 20 |        |   6 am |
|000006d0| 26 20 35 37 20 26 20 36 | 20 70 6d 20 26 20 39 36 |& 57 & 6| pm & 96|
|000006e0| 20 5c 5c 0a 20 20 20 20 | 20 20 20 20 20 20 20 20 | \\.    |        |
|000006f0| 20 20 20 20 37 20 61 6d | 20 26 20 36 34 20 26 20 |    7 am| & 64 & |
|00000700| 37 20 70 6d 20 26 20 38 | 36 20 5c 5c 0a 20 20 20 |7 pm & 8|6 \\.   |
|00000710| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 38 20 61 |        |     8 a|
|00000720| 6d 20 26 20 37 30 20 26 | 20 38 20 70 6d 20 26 20 |m & 70 &| 8 pm & |
|00000730| 38 31 20 5c 5c 0a 20 20 | 20 20 20 20 20 20 20 20 |81 \\.  |        |
|00000740| 20 20 20 20 20 20 39 20 | 61 6d 20 26 20 37 36 20 |      9 |am & 76 |
|00000750| 26 20 39 20 70 6d 20 26 | 20 5c 5c 0a 20 20 20 20 |& 9 pm &| \\.    |
|00000760| 20 20 20 20 20 20 20 20 | 20 20 20 20 31 30 61 6d |        |    10am|
|00000770| 20 26 20 38 30 20 26 20 | 31 30 70 6d 20 26 20 5c | & 80 & |10pm & \|
|00000780| 5c 0a 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |\.      |        |
|00000790| 20 20 31 31 61 6d 20 26 | 20 38 34 20 26 20 31 31 |  11am &| 84 & 11|
|000007a0| 70 6d 20 26 20 5c 5c 20 | 20 20 5c 68 6c 69 6e 65 |pm & \\ |  \hline|
|000007b0| 0a 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.       |        |
|000007c0| 20 5c 65 6e 64 7b 74 61 | 62 75 6c 61 72 7d 0a 20 | \end{ta|bular}. |
|000007d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 0a |        |       .|
|000007e0| 5c 76 73 70 61 63 65 7b | 31 20 65 78 7d 0a 5c 6e |\vspace{|1 ex}.\n|
|000007f0| 6f 69 6e 64 65 6e 74 20 | 46 69 72 73 74 2c 20 69 |oindent |First, i|
|00000800| 66 20 79 6f 75 20 61 72 | 65 20 6e 65 77 20 74 6f |f you ar|e new to|
|00000810| 20 43 6f 6c 6f 72 61 64 | 6f 2c 20 6e 6f 74 65 20 | Colorad|o, note |
|00000820| 74 68 65 20 74 65 6d 70 | 65 72 61 74 75 72 65 20 |the temp|erature |
|00000830| 72 61 6e 67 65 20 69 6e | 20 61 20 73 69 6e 67 6c |range in| a singl|
|00000840| 65 20 64 61 79 21 20 20 | 4e 65 78 74 3a 20 49 73 |e day!  |Next: Is|
|00000850| 20 54 65 6d 70 20 61 20 | 66 75 6e 63 74 69 6f 6e | Temp a |function|
|00000860| 20 6f 66 20 54 69 6d 65 | 3f 20 20 49 73 20 54 69 | of Time|?  Is Ti|
|00000870| 6d 65 20 61 20 66 75 6e | 63 74 69 6f 6e 20 6f 66 |me a fun|ction of|
|00000880| 20 54 65 6d 70 3f 20 20 | 49 66 20 79 6f 75 20 61 | Temp?  |If you a|
|00000890| 6e 73 77 65 72 65 64 20 | 60 60 79 65 73 27 27 20 |nswered |``yes'' |
|000008a0| 74 6f 20 65 69 74 68 65 | 72 20 6f 72 20 62 6f 74 |to eithe|r or bot|
|000008b0| 68 20 71 75 65 73 74 69 | 6f 6e 73 2c 20 77 68 61 |h questi|ons, wha|
|000008c0| 74 20 61 72 65 20 74 68 | 65 20 64 6f 6d 61 69 6e |t are th|e domain|
|000008d0| 73 20 61 6e 64 20 72 61 | 6e 67 65 73 3f 0a 0a 20 |s and ra|nges?.. |
|000008e0| 20 20 20 20 20 20 20 5c | 69 74 65 6d 20 54 68 65 |       \|item The|
|000008f0| 20 60 60 4e 65 76 65 72 | 20 6f 6e 20 53 75 6e 64 | ``Never| on Sund|
|00000900| 61 79 27 27 20 64 61 74 | 61 20 73 65 74 20 69 73 |ay'' dat|a set is|
|00000910| 3a 0a 0a 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |:..     |        |
|00000920| 20 20 20 5c 62 65 67 69 | 6e 7b 74 61 62 75 6c 61 |   \begi|n{tabula|
|00000930| 72 7d 7b 6c 7c 6c 7d 20 | 20 20 20 5c 68 6c 69 6e |r}{l|l} |   \hlin|
|00000940| 65 0a 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |e.      |        |
|00000950| 20 20 7b 5c 62 66 20 44 | 61 79 7d 20 26 20 7b 5c |  {\bf D|ay} & {\|
|00000960| 62 66 20 41 6e 73 77 65 | 72 7d 20 5c 5c 0a 20 20 |bf Answe|r} \\.  |
|00000970| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 53 75 |        |      Su|
|00000980| 6e 64 61 79 20 26 20 4e | 6f 20 5c 5c 0a 20 20 20 |nday & N|o \\.   |
|00000990| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 4d 6f 6e |        |     Mon|
|000009a0| 64 61 79 20 26 20 59 65 | 73 20 5c 5c 0a 20 20 20 |day & Ye|s \\.   |
|000009b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 54 75 65 |        |     Tue|
|000009c0| 73 64 61 79 20 26 20 59 | 65 73 20 5c 5c 0a 20 20 |sday & Y|es \\.  |
|000009d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 57 65 |        |      We|
|000009e0| 64 6e 65 73 64 61 79 20 | 26 20 59 65 73 20 5c 5c |dnesday |& Yes \\|
|000009f0| 0a 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.       |        |
|00000a00| 20 54 68 75 72 73 64 61 | 79 20 26 20 59 65 73 20 | Thursda|y & Yes |
|00000a10| 5c 5c 0a 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |\\.     |        |
|00000a20| 20 20 20 46 72 69 64 61 | 79 20 26 20 59 65 73 20 |   Frida|y & Yes |
|00000a30| 5c 5c 0a 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |\\.     |        |
|00000a40| 20 20 20 53 61 74 75 72 | 64 61 79 20 26 20 59 65 |   Satur|day & Ye|
|00000a50| 73 20 5c 5c 20 20 20 20 | 20 20 20 5c 68 6c 69 6e |s \\    |   \hlin|
|00000a60| 65 0a 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |e.      |        |
|00000a70| 20 20 5c 65 6e 64 7b 74 | 61 62 75 6c 61 72 7d 0a |  \end{t|abular}.|
|00000a80| 0a 5c 76 73 70 61 63 65 | 7b 31 20 65 78 7d 0a 5c |.\vspace|{1 ex}.\|
|00000a90| 6e 6f 69 6e 64 65 6e 74 | 20 49 73 20 41 6e 73 77 |noindent| Is Answ|
|00000aa0| 65 72 20 61 20 66 75 6e | 63 74 69 6f 6e 20 6f 66 |er a fun|ction of|
|00000ab0| 20 44 61 79 3f 20 20 49 | 73 20 44 61 79 20 61 20 | Day?  I|s Day a |
|00000ac0| 66 75 6e 63 74 69 6f 6e | 20 6f 66 20 41 6e 73 77 |function| of Answ|
|00000ad0| 65 72 3f 20 20 49 66 20 | 79 6f 75 20 61 6e 73 77 |er?  If |you answ|
|00000ae0| 65 72 65 64 20 60 60 79 | 65 73 27 27 20 74 6f 20 |ered ``y|es'' to |
|00000af0| 65 69 74 68 65 72 20 6f | 72 20 62 6f 74 68 20 71 |either o|r both q|
|00000b00| 75 65 73 74 69 6f 6e 73 | 2c 20 77 68 61 74 20 61 |uestions|, what a|
|00000b10| 72 65 20 74 68 65 20 64 | 6f 6d 61 69 6e 73 20 61 |re the d|omains a|
|00000b20| 6e 64 20 72 61 6e 67 65 | 73 3f 0a 20 20 20 20 20 |nd range|s?.     |
|00000b30| 20 20 20 5c 65 6e 64 7b | 65 6e 75 6d 65 72 61 74 |   \end{|enumerat|
|00000b40| 65 7d 0a 0a 5c 69 74 65 | 6d 20 46 75 6e 63 74 69 |e}..\ite|m Functi|
|00000b50| 6f 6e 73 20 63 61 6e 20 | 73 6f 6d 65 74 69 6d 65 |ons can |sometime|
|00000b60| 73 20 62 65 20 73 70 65 | 63 69 66 69 65 64 20 62 |s be spe|cified b|
|00000b70| 79 20 67 69 76 69 6e 67 | 20 28 64 6f 6d 61 69 6e |y giving| (domain|
|00000b80| 2c 20 72 61 6e 67 65 29 | 20 70 61 69 72 73 2e 20 |, range)| pairs. |
|00000b90| 0a 20 20 20 20 20 20 20 | 20 5c 62 65 67 69 6e 7b |.       | \begin{|
|00000ba0| 65 6e 75 6d 65 72 61 74 | 65 7d 0a 20 20 20 20 20 |enumerat|e}.     |
|00000bb0| 20 20 20 5c 69 74 65 6d | 20 49 73 20 74 68 69 73 |   \item| Is this|
|00000bc0| 20 20 73 65 74 20 6f 66 | 20 70 61 69 72 73 20 61 |  set of| pairs a|
|00000bd0| 20 66 75 6e 63 74 69 6f | 6e 3a 20 5c 7b 28 31 2c | functio|n: \{(1,|
|00000be0| 20 31 29 2c 20 28 32 2c | 20 32 29 2c 20 28 33 2c | 1), (2,| 2), (3,|
|00000bf0| 20 33 29 2c 20 28 34 2c | 20 34 29 2c 20 28 35 2c | 3), (4,| 4), (5,|
|00000c00| 20 35 29 5c 7d 20 20 49 | 66 20 79 6f 75 20 73 61 | 5)\}  I|f you sa|
|00000c10| 69 64 20 60 60 79 65 73 | 27 27 2c 20 64 6f 6d 61 |id ``yes|'', doma|
|00000c20| 69 6e 3f 20 72 61 6e 67 | 65 3f 0a 20 20 20 20 20 |in? rang|e?.     |
|00000c30| 20 20 20 5c 69 74 65 6d | 20 49 73 20 74 68 69 73 |   \item| Is this|
|00000c40| 20 73 65 74 20 6f 66 20 | 70 61 69 72 73 20 61 20 | set of |pairs a |
|00000c50| 66 75 6e 63 74 69 6f 6e | 3a 20 5c 7b 28 31 2c 20 |function|: \{(1, |
|00000c60| 31 29 2c 20 28 32 2c 20 | 32 29 2c 20 28 32 2c 20 |1), (2, |2), (2, |
|00000c70| 33 29 2c 20 28 34 2c 20 | 34 29 2c 20 28 31 2c 20 |3), (4, |4), (1, |
|00000c80| 35 29 5c 7d 20 20 49 66 | 20 79 6f 75 20 73 61 69 |5)\}  If| you sai|
|00000c90| 64 20 60 60 79 65 73 27 | 27 2c 20 64 6f 6d 61 69 |d ``yes'|', domai|
|00000ca0| 6e 3f 20 72 61 6e 67 65 | 3f 0a 20 20 20 20 20 20 |n? range|?.      |
|00000cb0| 20 20 5c 65 6e 64 7b 65 | 6e 75 6d 65 72 61 74 65 |  \end{e|numerate|
|00000cc0| 7d 0a 0a 5c 69 74 65 6d | 20 46 75 6e 63 74 69 6f |}..\item| Functio|
|00000cd0| 6e 73 20 63 61 6e 20 73 | 6f 6d 65 74 69 6d 65 73 |ns can s|ometimes|
|00000ce0| 20 62 65 20 73 70 65 63 | 69 66 69 65 64 20 62 79 | be spec|ified by|
|00000cf0| 20 61 20 67 72 61 70 68 | 2e 20 20 57 68 69 63 68 | a graph|.  Which|
|00000d00| 20 6f 66 20 74 68 65 20 | 66 6f 6c 6c 6f 77 69 6e | of the |followin|
|00000d10| 67 20 72 65 70 72 65 73 | 65 6e 74 20 61 20 66 75 |g repres|ent a fu|
|00000d20| 6e 63 74 69 6f 6e 20 24 | 79 20 3d 20 66 28 78 29 |nction $|y = f(x)|
|00000d30| 24 3f 20 20 49 73 20 69 | 74 20 66 65 61 73 69 62 |$?  Is i|t feasib|
|00000d40| 6c 65 20 74 6f 20 67 65 | 74 20 74 68 65 20 64 6f |le to ge|t the do|
|00000d50| 6d 61 69 6e 20 61 6e 64 | 20 72 61 6e 67 65 20 66 |main and| range f|
|00000d60| 72 6f 6d 20 74 68 65 20 | 67 72 61 70 68 3f 0a 20 |rom the |graph?. |
|00000d70| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 5c |        |       \|
|00000d80| 62 65 67 69 6e 7b 66 69 | 67 75 72 65 7d 5b 68 74 |begin{fi|gure}[ht|
|00000d90| 62 5d 0a 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |b].     |        |
|00000da0| 20 20 20 5c 65 70 73 66 | 79 73 69 7a 65 20 31 30 |   \epsf|ysize 10|
|00000db0| 30 70 74 0a 20 20 20 20 | 20 20 20 20 20 20 20 20 |0pt.    |        |
|00000dc0| 20 20 20 20 5c 63 65 6e | 74 65 72 6c 69 6e 65 7b |    \cen|terline{|
|00000dd0| 5c 65 70 73 66 66 69 6c | 65 7b 77 73 32 70 34 61 |\epsffil|e{ws2p4a|
|00000de0| 2e 65 70 73 7d 7d 0a 20 | 20 20 20 20 20 20 20 20 |.eps}}. |        |
|00000df0| 20 20 20 20 20 20 20 5c | 63 61 70 74 69 6f 6e 7b |       \|caption{|
|00000e00| 47 72 61 70 68 20 20 61 | 7d 20 0a 20 20 20 20 20 |Graph  a|} .     |
|00000e10| 20 20 20 20 20 20 20 20 | 20 20 20 5c 65 6e 64 7b |        |   \end{|
|00000e20| 66 69 67 75 72 65 7d 0a | 0a 20 20 20 20 20 20 20 |figure}.|.       |
|00000e30| 20 20 20 20 20 20 20 20 | 20 5c 62 65 67 69 6e 7b |        | \begin{|
|00000e40| 66 69 67 75 72 65 7d 5b | 68 62 74 5d 0a 20 20 20 |figure}[|hbt].   |
|00000e50| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 5c 65 70 |        |     \ep|
|00000e60| 73 66 79 73 69 7a 65 20 | 31 30 30 70 74 0a 20 20 |sfysize |100pt.  |
|00000e70| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 5c 63 |        |      \c|
|00000e80| 65 6e 74 65 72 6c 69 6e | 65 7b 5c 65 70 73 66 66 |enterlin|e{\epsff|
|00000e90| 69 6c 65 7b 77 73 32 70 | 34 62 2e 65 70 73 7d 7d |ile{ws2p|4b.eps}}|
|00000ea0| 0a 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.       |        |
|00000eb0| 20 5c 63 61 70 74 69 6f | 6e 7b 47 72 61 70 68 20 | \captio|n{Graph |
|00000ec0| 62 7d 20 0a 20 20 20 20 | 20 20 20 20 20 20 20 20 |b} .    |        |
|00000ed0| 20 20 20 20 5c 65 6e 64 | 7b 66 69 67 75 72 65 7d |    \end|{figure}|
|00000ee0| 0a 0a 5c 69 74 65 6d 20 | 20 46 75 6e 63 74 69 6f |..\item | Functio|
|00000ef0| 6e 73 20 63 61 6e 20 73 | 6f 6d 65 74 69 6d 65 73 |ns can s|ometimes|
|00000f00| 20 62 65 20 73 70 65 63 | 69 66 69 65 64 20 69 6e | be spec|ified in|
|00000f10| 20 77 6f 72 64 73 2e 0a | 20 20 20 20 20 20 20 20 | words..|        |
|00000f20| 5c 62 65 67 69 6e 7b 65 | 6e 75 6d 65 72 61 74 65 |\begin{e|numerate|
|00000f30| 7d 0a 20 20 20 20 20 20 | 20 20 5c 69 74 65 6d 20 |}.      |  \item |
|00000f40| 44 6f 65 73 20 60 60 74 | 68 65 20 73 74 72 61 69 |Does ``t|he strai|
|00000f50| 67 68 74 20 6c 69 6e 65 | 20 70 61 73 73 69 6e 67 |ght line| passing|
|00000f60| 20 74 68 72 6f 75 67 68 | 20 74 68 65 20 70 6f 69 | through| the poi|
|00000f70| 6e 74 73 20 28 31 2c 33 | 29 2c 20 28 36 2c 20 31 |nts (1,3|), (6, 1|
|00000f80| 32 29 27 27 20 64 65 73 | 63 72 69 62 65 20 61 20 |2)'' des|cribe a |
|00000f90| 66 75 6e 63 74 69 6f 6e | 3f 0a 20 20 20 20 20 20 |function|?.      |
|00000fa0| 20 20 5c 69 74 65 6d 20 | 57 68 61 74 20 61 62 6f |  \item |What abo|
|00000fb0| 75 74 20 60 60 74 68 65 | 20 63 69 72 63 6c 65 20 |ut ``the| circle |
|00000fc0| 77 69 74 68 20 63 65 6e | 74 65 72 20 28 33 2c 34 |with cen|ter (3,4|
|00000fd0| 29 20 61 6e 64 20 72 61 | 64 69 75 73 20 35 27 27 |) and ra|dius 5''|
|00000fe0| 3f 0a 20 20 20 20 20 20 | 20 20 5c 69 74 65 6d 20 |?.      |  \item |
|00000ff0| 48 6f 77 20 61 62 6f 75 | 74 20 60 60 74 68 65 20 |How abou|t ``the |
|00001000| 6d 6f 6e 74 68 6c 79 20 | 70 6f 70 75 6c 61 74 69 |monthly |populati|
|00001010| 6f 6e 20 6f 66 20 56 61 | 69 6c 2c 20 43 6f 6c 6f |on of Va|il, Colo|
|00001020| 72 61 64 6f 20 62 65 74 | 77 65 65 6e 20 31 39 35 |rado bet|ween 195|
|00001030| 30 20 61 6e 64 20 74 68 | 65 20 70 72 65 73 65 6e |0 and th|e presen|
|00001040| 74 27 27 3f 0a 20 20 20 | 20 20 20 20 20 5c 65 6e |t''?.   |     \en|
|00001050| 64 7b 65 6e 75 6d 65 72 | 61 74 65 7d 0a 0a 5c 69 |d{enumer|ate}..\i|
|00001060| 74 65 6d 20 57 65 6c 6c | 2c 20 65 76 65 6e 20 77 |tem Well|, even w|
|00001070| 69 74 68 20 61 6c 6c 20 | 74 68 65 73 65 20 61 6c |ith all |these al|
|00001080| 74 65 72 6e 61 74 69 76 | 65 73 2c 20 69 74 20 63 |ternativ|es, it c|
|00001090| 61 6e 27 74 20 62 65 20 | 64 65 6e 69 65 64 20 74 |an't be |denied t|
|000010a0| 68 61 74 20 61 20 66 6f | 72 6d 75 6c 61 20 69 73 |hat a fo|rmula is|
|000010b0| 20 61 20 75 73 65 66 75 | 6c 20 74 68 69 6e 67 2e | a usefu|l thing.|
|000010c0| 20 20 53 6f 20 6e 6f 77 | 2c 20 49 27 6c 6c 20 61 |  So now|, I'll a|
|000010d0| 73 6b 20 79 6f 75 20 66 | 6f 72 20 73 6f 6d 65 21 |sk you f|or some!|
|000010e0| 0a 0a 20 20 20 20 20 20 | 20 20 5c 62 65 67 69 6e |..      |  \begin|
|000010f0| 7b 65 6e 75 6d 65 72 61 | 74 65 7d 0a 20 20 20 20 |{enumera|te}.    |
|00001100| 20 20 20 20 5c 69 74 65 | 6d 20 41 20 73 74 72 61 |    \ite|m A stra|
|00001110| 69 67 68 74 20 6c 69 6e | 65 20 69 73 20 64 65 74 |ight lin|e is det|
|00001120| 65 72 6d 69 6e 65 64 20 | 62 79 20 74 77 6f 20 70 |ermined |by two p|
|00001130| 6f 69 6e 74 73 2c 20 72 | 69 67 68 74 3f 20 20 53 |oints, r|ight?  S|
|00001140| 6f 20 69 66 0a 20 20 20 | 20 20 20 20 20 20 20 20 |o if.   |        |
|00001150| 20 20 20 20 20 74 68 65 | 20 70 6f 69 6e 74 73 20 |     the| points |
|00001160| 61 72 65 20 24 50 5f 31 | 28 78 5f 31 2c 20 79 5f |are $P_1|(x_1, y_|
|00001170| 31 29 24 20 61 6e 64 20 | 24 50 5f 32 28 78 5f 32 |1)$ and |$P_2(x_2|
|00001180| 2c 20 79 5f 32 29 24 2c | 20 71 75 69 63 6b 0a 20 |, y_2)$,| quick. |
|00001190| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 6e |        |       n|
|000011a0| 6f 77 2c 20 77 72 69 74 | 65 20 61 20 66 6f 72 6d |ow, writ|e a form|
|000011b0| 75 6c 61 20 66 6f 72 20 | 74 68 65 20 73 74 72 61 |ula for |the stra|
|000011c0| 69 67 68 74 20 6c 69 6e | 65 2e 20 20 41 6e 79 20 |ight lin|e.  Any |
|000011d0| 73 70 65 63 69 61 6c 0a | 20 20 20 20 20 20 20 20 |special.|        |
|000011e0| 20 20 20 20 20 20 20 20 | 63 61 73 65 73 20 74 6f |        |cases to|
|000011f0| 20 6e 6f 74 65 3f 0a 20 | 20 20 20 20 20 20 20 0a | note?. |       .|
|00001200| 20 20 20 20 20 20 20 20 | 5c 69 74 65 6d 20 41 20 |        |\item A |
|00001210| 73 74 72 61 69 67 68 74 | 20 6c 69 6e 65 20 69 73 |straight| line is|
|00001220| 20 61 6c 73 6f 20 64 65 | 74 65 72 6d 69 6e 65 64 | also de|termined|
|00001230| 20 62 79 20 61 20 70 6f | 69 6e 74 20 61 6e 64 20 | by a po|int and |
|00001240| 61 20 73 6c 6f 70 65 2e | 20 20 53 6f 20 69 66 20 |a slope.|  So if |
|00001250| 74 68 65 20 70 6f 69 6e | 74 20 69 73 20 24 50 5f |the poin|t is $P_|
|00001260| 31 28 78 5f 31 2c 20 79 | 5f 31 29 24 20 61 6e 64 |1(x_1, y|_1)$ and|
|00001270| 20 74 68 65 20 73 6c 6f | 70 65 20 69 73 20 24 6d | the slo|pe is $m|
|00001280| 24 2c 20 77 72 69 74 65 | 20 61 20 66 6f 72 6d 75 |$, write| a formu|
|00001290| 6c 61 20 66 6f 72 20 74 | 68 65 20 73 74 72 61 69 |la for t|he strai|
|000012a0| 67 68 74 20 6c 69 6e 65 | 2e 0a 20 20 20 20 20 20 |ght line|..      |
|000012b0| 20 20 0a 20 20 20 20 20 | 20 20 20 5c 69 74 65 6d |  .     |   \item|
|000012c0| 20 41 20 73 74 72 61 69 | 67 68 74 20 6c 69 6e 65 | A strai|ght line|
|000012d0| 20 69 73 20 61 6c 73 6f | 20 64 65 74 65 72 6d 69 | is also| determi|
|000012e0| 6e 65 64 20 62 79 20 69 | 74 73 20 73 6c 6f 70 65 |ned by i|ts slope|
|000012f0| 20 61 6e 64 20 60 60 69 | 6e 74 65 72 63 65 70 74 | and ``i|ntercept|
|00001300| 27 27 2e 20 20 42 75 74 | 20 69 73 6e 27 74 20 74 |''.  But| isn't t|
|00001310| 68 69 73 20 6a 75 73 74 | 20 61 20 73 70 65 63 69 |his just| a speci|
|00001320| 61 6c 20 63 61 73 65 20 | 6f 66 20 74 68 65 20 70 |al case |of the p|
|00001330| 72 65 76 69 6f 75 73 20 | 63 61 73 65 3f 20 20 41 |revious |case?  A|
|00001340| 6e 79 77 61 79 2c 20 69 | 66 20 74 68 65 20 73 6c |nyway, i|f the sl|
|00001350| 6f 70 65 20 69 73 20 24 | 6d 24 20 61 6e 64 20 74 |ope is $|m$ and t|
|00001360| 68 65 20 24 79 24 2d 69 | 6e 74 65 72 63 65 70 74 |he $y$-i|ntercept|
|00001370| 20 69 73 20 24 62 24 2c | 20 77 72 69 74 65 20 64 | is $b$,| write d|
|00001380| 6f 77 6e 20 61 20 66 6f | 72 6d 75 6c 61 20 66 6f |own a fo|rmula fo|
|00001390| 72 20 74 68 65 20 73 74 | 72 61 69 67 68 74 20 6c |r the st|raight l|
|000013a0| 69 6e 65 2e 0a 20 20 20 | 20 20 20 20 20 5c 65 6e |ine..   |     \en|
|000013b0| 64 7b 65 6e 75 6d 65 72 | 61 74 65 7d 0a 0a 5c 65 |d{enumer|ate}..\e|
|000013c0| 6e 64 7b 65 6e 75 6d 65 | 72 61 74 65 7d 0a 5c 65 |nd{enume|rate}.\e|
|000013d0| 6e 64 7b 64 6f 63 75 6d | 65 6e 74 7d 0a          |nd{docum|ent}.   |
+--------+-------------------------+-------------------------+--------+--------+