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# Diff of /trunk/NationalProblemLibrary/LoyolaChicago/Precalc/Chap9Sec5/Q06.pg

Revision 2460 Revision 2461
10## TitleText1('Functions Modeling Change') 10## TitleText1('Functions Modeling Change')
11## EditionText1('3') 11## EditionText1('3')
12## AuthorText1('Connally') 12## AuthorText1('Connally')
13## Section1('9.5) 13## Section1('9.5)
14## Problem1('6') 14## Problem1('6')
15## TitleText2('Functions Modeling Change');
16## EditionText2('4')
17## AuthorText2('Connally')
18## Section2('11.5')
19## Problem2('8')
15## Author('Adam Spiegler and Paul Pearson') 20## Author('Adam Spiegler and Paul Pearson')
16## Institution('Loyola University Chicago and Fort Lewis College') 21## Institution('Loyola University Chicago and Fort Lewis College')
17 22
18DOCUMENT(); 23DOCUMENT();
19 24
21 "PGbasicmacros.pl", 26 "PGbasicmacros.pl",
22# "PGchoicemacros.pl", 27# "PGchoicemacros.pl",
27"MathObjects.pl", 32"MathObjects.pl",
29"PGcourse.pl", 34"PGcourse.pl",
30 ); 35 );
31 36
32TEXT(beginproblem()); # standard preamble to each problem. 37TEXT(beginproblem());
33 38
34Context("Numeric"); 39Context("Numeric");
35 40
36$showPartialCorrectAnswers = 1; 41$showPartialCorrectAnswers = 1;
37 42
51} 56}
52 57
53$yint = List(-1); 58$yint = List(-1);
54$hor = List(1); 59$hor = List(1);
55 60
56 61Context()->texStrings;
57
58BEGIN_TEXT 62BEGIN_TEXT
59Find all zeros and vertical asymptotes of the rational function 63Find all zeros and vertical asymptotes of the rational function
60$BR 64$PAR
61$BR 62$$\displaystyle f(x) = eqn$$. 65$$\displaystyle f(x) = eqn$$. 63$BR 66$PAR 64$BR
65If there is more than one answer, enter your answers as a comma separated list. If there is no solution, enter ${BITALIC}NONE.${EITALIC} Do not leave a blank empty. 67If there is more than one answer, enter your answers as a comma separated list. If there is no solution, enter ${BITALIC}NONE.${EITALIC} Do not leave a blank empty.
66$BR 68$PAR
67$BR 68(a) The function has x-intercept(s) at $$x =$$ \{ ans_rule(20) \} 69(a) The function has x-intercept(s) at $$x =$$ \{ ans_rule(20) \} 69\{ AnswerFormatHelp("numbers") \} 70\{ AnswerFormatHelp("numbers") \} 70$BR 71$PAR 71$BR
72(b) The function has y-intercept(s) at $$y =$$ \{ ans_rule(20) \} 72(b) The function has y-intercept(s) at $$y =$$ \{ ans_rule(20) \}
74$BR 74$PAR
75$BR 76(c) The function has vertical asymptote(s) when $$x =$$ \{ ans_rule(20) \} 75(c) The function has vertical asymptote(s) when $$x =$$ \{ ans_rule(20) \} 77\{ AnswerFormatHelp("numbers") \} 76\{ AnswerFormatHelp("numbers") \} 78$BR 77$PAR 79$BR
80(d) The function has horizontal asymptote(s) when $$y =$$ \{ ans_rule(20) \} 78(d) The function has horizontal asymptote(s) when $$y =$$ \{ ans_rule(20) \}
82END_TEXT 80END_TEXT
81Context()->normalStrings;
83 82
84 83
85#if ($i == 0) { 84#if ($i == 0) {
86 85
87ANS($zero->cmp(showLengthHints=>1) ); 86ANS($zero->cmp(showLengthHints=>1) );
88ANS($yint->cmp(showLengthHints=>1) ); 87ANS($yint->cmp(showLengthHints=>1) );
89ANS($vert->cmp(showLengthHints=>1) ); 88ANS($vert->cmp(showLengthHints=>1) );
90ANS($hor ->cmp(showLengthHints=>1) ); 89ANS($hor ->cmp(showLengthHints=>1) );
91 90
92#} else { 91#} else {
93 92
94#ANS(List("$zero")->cmp(showLengthHints=>1) ); 93#ANS(List("$zero")->cmp(showLengthHints=>1) );
95#ANS(List("$yint")->cmp(showLengthHints=>1) ); 94#ANS(List("$yint")->cmp(showLengthHints=>1) );
103$explain = "Since $$\displaystyle g(x) = \frac{x^2-k}{x^2+k} = \frac{(x-b)(x+b)}{x^2+k}$$ the $$x$$-intercepts are $$x= \pm b$$; the $$y$$-intercept is $$y = -k/k =-1$$; the horizontal asymptote is $$y=1$$; there are no vertical asymptotes."} 102$explain = "Since $$\displaystyle g(x) = \frac{x^2-k}{x^2+k} = \frac{(x-b)(x+b)}{x^2+k}$$ the $$x$$-intercepts are $$x= \pm b$$; the $$y$$-intercept is $$y = -k/k =-1$$; the horizontal asymptote is $$y=1$$; there are no vertical asymptotes."}
104else { 103else {
105$explain = "Since $$\displaystyle g(x) = \frac{x^2+k}{x^2-k} = \frac{x^2+k}{(x-b)(x+b)}$$ the vertical asymptotes are at $$x= \pm b$$; the $$y$$-intercept is $$y = k/-k =-1$$; the horizontal asymptote is $$y=1$$; there are no $$x$$-intercepts."}; 104$explain = "Since $$\displaystyle g(x) = \frac{x^2+k}{x^2-k} = \frac{x^2+k}{(x-b)(x+b)}$$ the vertical asymptotes are at $$x= \pm b$$; the $$y$$-intercept is $$y = k/-k =-1$$; the horizontal asymptote is $$y=1$$; there are no $$x$$-intercepts."};
106 105
107 106
107Context()->texStrings;
108SOLUTION(EV3(<<'END_SOLUTION')); 108SOLUTION(EV3(<<'END_SOLUTION'));
109$BR$SPACE $BR 109$PAR
110$BBOLD SOLUTION$EBOLD 110$BBOLD SOLUTION$EBOLD
111$BR 111$PAR
112$explain 112$explain
113\$BR 113
114END_SOLUTION 114END_SOLUTION
115Context()->normalStrings;
115 116
116 117
117 118
118COMMENT('MathObject version'); 119COMMENT('MathObject version');
119ENDDOCUMENT(); 120ENDDOCUMENT();

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