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# View of /branches/Rogawski_Calculus/2e/1_Precalculus_Review/1.1_Real_Numbers_Functions,_Equations_and_Graphs/1.1.71

Wed Feb 2 15:17:38 2011 UTC (2 years, 3 months ago) by whfreeman
File size: 2738 byte(s)
update

    1 ## DBsubject('Algebra')
2 ## DBchapter('Functions')
3 ## DBsection('Domain and Range')
4 ## KEYWORDS('calculus', 'intervals','domain', 'range', 'functions')
5 ## TitleText1('Calculus: Early Transcendentals')
6 ## EditionText1('2')
7 ## AuthorText1('Rogawski')
8 ## Section1('1.1')
9 ## Problem1('71')
10 ## Author('Carol Panepinto')
11 ## Institution('W.H.Freeman')
12
13 DOCUMENT();
17
18 $x = random(3,10); 19$y = random(11,20);
20 $z = random(1,8); 21$k = random(9,18);
22
23 $a = Interval("[$x,$y]"); 24$b = Interval("[($z),($k)]");
25
26 $n = random(2,5); 27 28$ansad = Interval("[($x),($y)]");
29 $ansar = Interval("[($z+$n),($k+$n)]"); 30$solarx = Formula($z+$n);
31 $solary = Formula($k+$n); 32 33$ansbd = Interval("[$x-$n,$y-$n]");
34 $ansbr = Interval("[$z,$k]"); 35$solbdx = Formula($x-$n);
36 $solbdy = Formula($y-$n); 37 38$anscd = Interval("[$x/$n,$y/$n]");
39 $anscr = Interval("[$z,$k]"); 40 41$ansdd = Interval("[$x,$y]");
42 $ansdr = Interval("[$n*$z,$n*$k]"); 43$soldd = Formula($n*$z);
44 $soldr = Formula($n*$k); 45 46 Context()->texStrings; 47 BEGIN_TEXT 48 \{ beginproblem() \} 49 \{ textbook_ref_exact("Rogawski ET 2e", "1.1","71") \} 50$PAR
51 Suppose that $$f(x)$$ has a domain of $$a$$ and a range of $$b$$.  What are the domain and range of:$PAR 52 (a)$BBOLD $$f(x) + n$$ $SPACE 53 Domain$EBOLD \{ans_rule(10)\} $SPACE 54$BBOLD Range $EBOLD \{ans_rule(10)\}$PAR
55
56 (b) $$f(x+n)$$ $SPACE 57$BBOLD Domain \{ans_rule(10)\} $SPACE 58 Range$EBOLD \{ans_rule(10)\}  $PAR 59 60 61 (c) $$f(n x)$$$SPACE $SPACE$SPACE $SPACE 62$BBOLD Domain \{ans_rule(10)\}  $SPACE 63 Range$EBOLD \{ans_rule(10)\}  $PAR 64 65 (d) $$n f(x)$$$SPACE $SPACE$SPACE $SPACE 66$BBOLD Domain \{ans_rule(10)\}  $SPACE 67 Range$EBOLD \{ans_rule(10)\}  $PAR 68 69 70$PAR
71
72 END_TEXT
73 Context()->normalStrings;
74
75 ANS($ansad->cmp); 76 ANS($ansar->cmp);
77 ANS($ansbd->cmp); 78 ANS($ansbr->cmp);
79 ANS($anscd->cmp); 80 ANS($anscr->cmp);
81 ANS($ansdd->cmp); 82 ANS($ansdr->cmp);
83
84 Context()->texStrings;
85 SOLUTION(EV3(<<'END_SOLUTION'));
86 $PAR 87$SOL
88 $PAR 89 (a) $$f(x)+n$$ is obtained by shifting $$f(x)$$ upwards by $$n$$ units. Therefore the domain remains $$[x,y]$$ while the range becomes $$[solarx, solary]$$. 90$PAR
91 (b) $$f(x+n)$$ is obtained by shifting $$f(x)$$ by $$n$$ units left along the x axis.  Therefore the domain becomes $$[solbdx, solbdy]$$ while the range remains $$[z, k]$$.
92 $PAR 93 (c) $$f(n x)$$ is obtained by compressing $$f(x)$$ by a factor of $$n$$. Therefore the domain becomes $$[\frac{x}{n},\frac{y}{n}]$$ while the range remains $$[z,k]$$. 94$PAR
95 (d) $$n f(x)$$ is obtained by stretching $$f(x)$$ vertically by a factor of $$n$$.  Therefore the domain remains $$[x,y]$$ while the range becomes $$[soldd, soldr]$$.
96 \$PAR
97 END_SOLUTION
98
99 ENDDOCUMENT();