View of /trunk/NationalProblemLibrary/LoyolaChicago/Precalc/Chap9Sec5/Q06.pg

    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 
   25 loadMacros("PG.pl",
   26            "PGbasicmacros.pl",
   27 #           "PGchoicemacros.pl",
   28            "PGanswermacros.pl",
   29 #           "PGgraphmacros.pl",
   30 #           "PGauxiliaryFunctions.pl",
   31 #           "extraAnswerEvaluators.pl",
   32 "MathObjects.pl",
   33 "AnswerFormatHelp.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) \}
   70 \{ AnswerFormatHelp("numbers") \}
   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) \}
   76 \{ AnswerFormatHelp("numbers") \}
   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();