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Fri Oct 7 16:42:13 2011 UTC (19 months, 1 week ago) by glarose
File size: 3351 byte(s)
LoyolaChicago 9.5: 4e tagging, updates.

    1 # DESCRIPTION
2 # Problem from Functions Modeling Change, Connally et al., 3rd ed.
3 # WeBWorK problem written by Adam Spiegler, <aspiegler@luc.edu>
4 # ENDDESCRIPTION
5
6 ## DBsubject('Precalculus')
7 ## DBchapter('Polynomial And Rational Functions')
8 ## DBsection('The Short-Run Behavior Of Rational Functions')
9 ## KEYWORDS('rational','fraction','polynomial,'asymptote','intercept')
10 ## TitleText1('Functions Modeling Change')
11 ## EditionText1('3')
12 ## AuthorText1('Connally')
13 ## Section1('9.5)
14 ## Problem1('6')
15 ## TitleText2('Functions Modeling Change');
16 ## EditionText2('4')
17 ## AuthorText2('Connally')
18 ## Section2('11.5')
19 ## Problem2('8')
20 ## Author('Adam Spiegler and Paul Pearson')
21 ## Institution('Loyola University Chicago and Fort Lewis College')
22
23 DOCUMENT();
24
26            "PGbasicmacros.pl",
27 #           "PGchoicemacros.pl",
29 #           "PGgraphmacros.pl",
30 #           "PGauxiliaryFunctions.pl",
32 "MathObjects.pl",
34 "PGcourse.pl",
35            );
36
37 TEXT(beginproblem());
38
39 Context("Numeric");
40
41 $showPartialCorrectAnswers = 1; 42 43$i = random(0,1,1);
44 $b = random(1,6,1); 45$k = $b**2; 46 47$i = 0;
48 if ($i == 0) { 49$eqn = "\frac{x^2-$k}{x^2+$k}";
50       $zero = List($b,-$b); 51$vert = List("NONE");
52 } else {
53       $eqn = "\frac{x^2+$k}{x^2-$k}"; 54$vert = List($b,-$b);
55       $zero = List("NONE"); 56 } 57 58$yint = List(-1);
59 $hor = List(1); 60 61 Context()->texStrings; 62 BEGIN_TEXT 63 Find all zeros and vertical asymptotes of the rational function 64$PAR
65 $$\displaystyle f(x) = eqn$$.
66 $PAR 67 If there is more than one answer, enter your answers as a comma separated list. If there is no solution, enter${BITALIC}NONE.${EITALIC} Do not leave a blank empty. 68$PAR
69 (a) The function has x-intercept(s) at $$x =$$ \{ ans_rule(20) \}
71 $PAR 72 (b) The function has y-intercept(s) at $$y =$$ \{ ans_rule(20) \} 73 \{ AnswerFormatHelp("numbers") \} 74$PAR
75 (c) The function has vertical asymptote(s) when $$x =$$ \{ ans_rule(20) \}
77 $PAR 78 (d) The function has horizontal asymptote(s) when $$y =$$ \{ ans_rule(20) \} 79 \{ AnswerFormatHelp("numbers") \} 80 END_TEXT 81 Context()->normalStrings; 82 83 84 #if ($i == 0) {
85
86 ANS( $zero->cmp(showLengthHints=>1) ); 87 ANS($yint->cmp(showLengthHints=>1) );
88 ANS( $vert->cmp(showLengthHints=>1) ); 89 ANS($hor ->cmp(showLengthHints=>1) );
90
91 #} else {
92
93 #ANS(List("$zero")->cmp(showLengthHints=>1) ); 94 #ANS(List("$yint")->cmp(showLengthHints=>1) );
95 #ANS(List("$vert")->cmp(showLengthHints=>1) ); 96 #ANS(List("$hor") ->cmp(showLengthHints=>1) );
97
98 #}
99
100
101 if ($i == 0) { 102$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."}
103 else {
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."}; 105 106 107 Context()->texStrings; 108 SOLUTION(EV3(<<'END_SOLUTION')); 109$PAR
110 $BBOLD SOLUTION$EBOLD
111 $PAR 112$explain
113
114 END_SOLUTION
115 Context()->normalStrings;
116
117
118
119 COMMENT('MathObject version');
120 ENDDOCUMENT();